user279: What's the technique behind the moves of the stronger side in order to win?
Are there situations where the side with K+R can force a draw against K+Q?
I've read plenty of examples of K+Q vs K+R, but they were only mere sequences of moves without explanation, and sometimes I didn't get the logic. The only thing I managed to understand is that the stronger side has to force the Rook away from his King, and then double-attack them with the Queen. But how can I make it happen?

user11261: Found this resource on the topic, which explains the three concrete steps involved in playing this endgame. Sharing here as it may help someone: http://www.chess-insights.com/queen-vs-rook.html
The linked article gives detailed explanation with good diagrams for each step. But to summarize in 3 sentences, the steps mentioned are as follows: 

First: force the rook into a third-rank defence and break that down. The defender then has to opt for a second-rank defence. 
Second: play against the second-rank defence until you reach the Philidor position. 
Third: win the rook from the Philidor Position.


user20949: I find Secrets of Pawnless Endings (Gambit, 2002) by John Nunn (pages 49 to 69) to be the ultimate reference about the KQvKR ending. All steps needed to force Philidor's 1777 position are described precisely, each position showing how to reduce to a previously seen position.
The book of course covers stalemate cases (which are all obvious) and what I call "perpetual check attractors", that is, positions that allow the KR side to force a position where the R will be able to give perpetual check.

user12533: I've done a lot of research on this ending, as I was a little downcast to see so few good resources showing the technique. I've summarised my findings in two articles on my page:
The ending is broken down into two elements - 
1. Winning from the Philidor position http://www.thequietmove.com/queen-v-rook-ending-philidor/ and
2. How to get to the Philidor position from an open board http://www.thequietmove.com/queen-v-rook-getting-to-philidor/ 
Note you really have to know the Philidor win or rely on tactics and this ending is super-tough! Happy chessing

user35: One possibility is to force a draw by repetition. E.g. if you have black Ka8, Qc8 and white Kb1, Rb2, then white needs just to check the black king forever. If he goes on the c file, the queen is lost. 
[fen "k1q5/8/8/8/8/8/1R6/1K6 w - - 0 1"]


user342: Goals in KR KQ:
Get your king to where you are attacking his rook.
Force his king to defend the rook while you attack it.
Remove the king as a defender from the rook with your queen.
Do not allow your queen in a position where a rook could attack it with support of the king unless you initiated a check.

user52: As long as we're mentioning ways the player with the rook can draw, the following is a very common setup in endgame puzzle books:
[fen "8/8/8/8/8/2QK4/8/3kr3 b - - 0 1"]

Black to move and draw
Solution:

 White is threatening to mate at c2, d2, and a1.  Black's only move is 1.. Re3+! 2. Kxe3 1/2-1/2


user103: There are a few technical ways to approach this endgame, the most notable one being a Philidor's Position (the KQ vs. KR one, not the KRP vs. KR one or the KRB vs. KR one).
If you do a web search for 3rd or 4th rank defense, you should be able to find more complicated situations outlining ideas for how the defensive position can try to put up a fight while minimizing the effects of a K-R fork occurring.

user17: In "Chess Fundamentals," former world champion J. R. Capablanca noted that this was the hardest of the basic piece-only endgames to win.
His analysis was that the stronger side can win if it can force the rook away from the king, with double threats of checkmating the king, and forking rook and king. If the defending side can keep the rook near the king without getting checkmated, it can draw. Often, the win or draw is just a matter of a square or two; e.g., the rook's staying on the same or opposite square color as the king (it is easier to fork them in the former case).

user2359: There are several key positions from which it is easy to memorize the win. The basic idea is to drive the opposing king to the edge of the board, and then to the corner, where you can force the rook to separate from the king.


[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "King and Queen"]
[Black "King and Rook"]
[Result "*"]
[SetUp "1"]
[FEN "8/6rk/5K2/3Q4/8/8/8/8 w - - 0 0"]
[PlyCount "11"]

1. Qh1+ (1. Qh5+? Kg8 {this is the diagram we want, but the wrong side has the
move.}) 1... Kg8 2. Qh5 {This is the key position to have with black to move.
The rook must leave the king} Rg1 (2... Kf8? 3.Qh6) 3. Qd5+ Kh7 4. Qe4+ Kg8 5. Qa8+ Kh7 6. Qa7+ {
forks the king and rook} *



The first move in the diagram is Qh1+. Qh5+? is a mistake, though the position is the one we want the wrong side is to move.
After 2.Qh5 we have the position we want. The rook must leave the protection of the king, and a series of checks will allow a fork of king and rook by the queen.
If the rook is already separated, then there is usually a sequence of checks that produce the win.


[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "King and Queen"]
[Black "King and Rook"]
[Result "*"]
[SetUp "1"]
[FEN "8/8/8/4K3/r6k/8/3Q4/8 w - - 0 3"]
[PlyCount "9"]

3. Kf5 Kg3 4. Qd3+ Kh4 5. Qc2 Ra5+ 6. Kf4 Kh3 7. Qc3+ *




user2042: 
INTRODUCTORY NOTE:
Examples and instructions are taken from the book:
Y.Averbakh - Comprehensive Chess Endings Volume 3.
In many cases I felt no need to "reinvent the wheel" so I quoted the above authors. Those parts will be marked with apostrophes "", like this: "This is a quoted text".

Without further delay let us tackle this endgame:
"In endings of this group the stronger side normally wins thanks to its big material advantage. At the same time, in a number of positions the rook's fighting quality enables it to put up a successful defense. Drawing dangers arise each time that the weaker side's  king, on being pushed to the edge of the board, becomes restricted in its mobility"-emphasis are mine.
So let us first start with the position in which rook can successfully defend.
[Title "Weaker side holds balance: Ponziani, 1782"]
[StartFlipped "0"]
[fen "5k2/6r1/4Q3/8/8/8/8/7K b - - 0 1"]

1...Rh7+ 2.Kg2 Rg7+ 3.Kf3 Rf7+ 4.Kg4 Rg7+ 5.Kf5 Rf7+ 6.Kg6 Rg7+ 7.Kh6 Rh7+! 8.Kxh7 1/2-1/2

Here is another relevant position:
[Title "Weaker side holds balance: Berger, 1889"]
[StartFlipped "0"]
[fen "6k1/6r1/5Q2/8/8/8/8/7K b - - 0 1"]

1...Rh7+ 2.Kg2 Rg7+ 3.Kh3 Rh7+ 4.Kg4 Rg7+ 5.Kh5 Rh7+ 6. Kg5 ( 6.Kg6 Rh6+! 7.Kxh6= ) 6...Rg7+ 7.Kh6 Rh7+ 8.Kg6 Rh6+! 9.Kxh6 1/2-1/2

Another important note from the authors:
"If, for example, the queen is moved to f1,f2,f3 or f4, the game ends in a perpetual check, since the king can not cross the f-file. But with his queen at f5 White wins: when his king occupies the h6 the rook does not have a saving check on h7."
Let us move on to another important position, and again I will quote the authors:
"If the queen is stalemating the king in the corner of the board, the rook may become a desperado."
The following example shows a badly posted rook trying to save the game in this manner.
[Title "Failed 'desperado' attempt"]
[StartFlipped "0"]
[fen "r6k/5Q2/2K5/8/8/8/8/8 b - - 0 1"]

1...Ra6+ 2.Kc5 Ra5+ ( 2...Rc6+ 3.Kd4 Rd6+ 4.Ke5+- ) 3.Kd4 Ra4+ 4.Kc3 Ra3+ 5.Kb2+-

Stronger side should maneuver with its king so that one of the checking squares is covered with the queen-this way queen can take the rook which frees opposing king from stalemate. King should approach the rook along a diagonal adjacent to the queen's.
Now let us see how weaker side defends when rook is properly posted:
[Title "Drawn for any position of the White king!"]
[StartFlipped "0"]
[fen "7k/5Q2/2K5/8/8/8/8/r7 b - - 0 1"]

1...Rc1+ 2.Kd5 ( 2.Kd6 Rd1+ 3.Ke6 Re1+ 4.Kd7 Rd1+ 5.Ke8 Rd8+! ( 5...Re1+?? 6.Kf8+- ) 6.Ke7 Rd7+ 7.Kxd7=) 2...Rd1+! ( 2...Rc5+?? 3.Kd4+- ) 3.Kc5 Rc1+ 4.Kb4 Rb1+ 5.Ka3 Ra1+ 6.Kb2 Rb1+ 7.Kc2 Rc1+=

Perpetual check! Do not forget that in this position rook must never leave the first rank! See the sub variation for the second Black's move ( 2...Rc5+?? 3.Kd4+- ).
Now let us move the rook on the g-file:
Do not forget that here rook must not leave the g-file!!
[Title "Drawn for any position of the White king!"]
[StartFlipped "0"]
[fen "6rk/5Q2/8/8/8/2K/8/8 b - - 0 1"]

1...Rg3+ 2.Kd4 Rg4+ 3.Ke5 Rg5+ 4.Ke6 ( 4.Kf6 Rf5+!= ) ( 4.Kd6 Rg6+= ) 4...Rg6+! 1/2-1/2

Let us sum up: In these types of positions the defender draws if his rook operates along the g-file or the 1st rank. Of course, this also applies for all 8 mirror positions.
For further details of playing these positions refer to the above book. In normal situations the queen always wins against a rook, although not without overcoming certain technical difficulties.
"The winning plan consists of pushing the opponent's king into the corner or onto the edge of the board and creating mating threats. In defending, the weaker side is forced to separate his forces, which leads to the loss of the rook by coming under double attack by the queen. The basic method of achieving the goal is zugzwang."
[Title "Stronger side wins: Philidor position"]
[StartFlipped "0"]
[fen "1k6/1r6/2K5/Q7/8/8/8/8 b - - 0 1"]

1...Rh7 ( 1...Rb1 2.Qd8+ Ka7 3.Qd4+ Ka8 4.Qh8+ Rb8 ( 4...Ka7 5.Qh7+ Ka8 6.Qxb1+- ) 5.Qa1# )  ) 2.Qe5+ Ka8 3.Qa1+! Kb8 4.Qb1+ Ka8 5.Qxh7+- 

If stronger side is to move, it gives back the move to the weaker side with the following maneuver:
[Title "Stronger side wins: Philidor position"]
[StartFlipped "0"]
[fen "1k6/1r6/2K5/Q7/8/8/8/8 w - - 0 1"]

1.Qe5+ Ka8 2.Qa1+! Kb8 ( 2...Ra7 3.Qh8# ) 3.Qa5+-

This maneuver is characteristic for this endgame.
The authors continue with practical examples of driving the weaker side's king to the edge/corner of the board but give no written instructions on how to achieve this.
This is not satisfactory for my standards thus I have tried to find a better resource for this. I believe this is decent coverage for the plan of pushing weaker side's king to the edge/corner of the board. Just look articles for second and third rank defense. If I find anything better I will edit my post, but for now this is the best I can find.
Best regards.

279: <p>What's the <em>technique</em> behind the moves of the stronger side in order to win?</p>

<p>Are there situations where the side with K+R can force a draw against K+Q?</p>

<p>I've read plenty of examples of K+Q vs K+R, but they were only mere sequences of moves without explanation, and sometimes I didn't get the logic. The only thing I managed to understand is that the stronger side has to force the Rook away from his King, and then double-attack them with the Queen. But how can I make it happen?</p>
 11261: <p>Found this resource on the topic, which explains the three concrete steps involved in playing this endgame. Sharing here as it may help someone: <a href="http://www.chess-insights.com/queen-vs-rook.html" rel="nofollow noreferrer">http://www.chess-insights.com/queen-vs-rook.html</a></p>

<p>The linked article gives detailed explanation with good diagrams for each step. But to summarize in 3 sentences, the steps mentioned are as follows: </p>

<ul>
<li><p>First: force the rook into a third-rank defence and break that down. The defender then has to opt for a second-rank defence. </p></li>
<li><p>Second: play against the second-rank defence until you reach the Philidor position. </p></li>
<li><p>Third: win the rook from the Philidor Position.</p></li>
</ul>
 20949: <p>I find <em>Secrets of Pawnless Endings</em> (Gambit, 2002) by John Nunn (pages 49 to 69) to be the ultimate reference about the KQvKR ending. All steps needed to force Philidor's 1777 position are described precisely, each position showing how to reduce to a previously seen position.</p>

<p>The book of course covers stalemate cases (which are all obvious) and what I call "perpetual check attractors", that is, positions that allow the KR side to force a position where the R will be able to give perpetual check.</p>
 12533: <p>I've done a lot of research on this ending, as I was a little downcast to see so few good resources showing the technique. I've summarised my findings in two articles on my page:</p>

<p>The ending is broken down into two elements - 
1. Winning from the Philidor position <a href="http://www.thequietmove.com/queen-v-rook-ending-philidor/" rel="nofollow noreferrer">http://www.thequietmove.com/queen-v-rook-ending-philidor/</a> and
2. How to get to the Philidor position from an open board <a href="http://www.thequietmove.com/queen-v-rook-getting-to-philidor/" rel="nofollow noreferrer">http://www.thequietmove.com/queen-v-rook-getting-to-philidor/</a> </p>

<p>Note you really have to know the Philidor win or rely on tactics and this ending is super-tough! Happy chessing</p>
 35: <p>One possibility is to force a draw by repetition. E.g. if you have black Ka8, Qc8 and white Kb1, Rb2, then white needs just to check the black king forever. If he goes on the c file, the queen is lost. </p>

<pre><code>[fen "k1q5/8/8/8/8/8/1R6/1K6 w - - 0 1"]
</code></pre>
 342: <p>Goals in KR KQ:</p>

<p>Get your king to where you are attacking his rook.</p>

<p>Force his king to defend the rook while you attack it.</p>

<p>Remove the king as a defender from the rook with your queen.</p>

<p>Do not allow your queen in a position where a rook could attack it with support of the king unless you initiated a check.</p>
 52: <p>As long as we're mentioning ways the player with the rook can draw, the following is a very common setup in endgame puzzle books:</p>

<pre><code>[fen "8/8/8/8/8/2QK4/8/3kr3 b - - 0 1"]
</code></pre>

<p><em>Black to move and draw</em></p>

<p>Solution:</p>

<blockquote class="spoiler">
  <p> White is threatening to mate at c2, d2, and a1.  Black's <em>only</em> move is 1.. Re3+! 2. Kxe3 1/2-1/2</p>
</blockquote>
 103: <p>There are a few technical ways to approach this endgame, the most notable one being a <a href="http://en.wikipedia.org/wiki/Philidor_position">Philidor's Position</a> (the KQ vs. KR one, not the KRP vs. KR one or the KRB vs. KR one).</p>

<p>If you do a web search for 3rd or 4th rank defense, you should be able to find more complicated situations outlining ideas for how the defensive position can try to put up a fight while minimizing the effects of a K-R fork occurring.</p>
 17: <p>In "Chess Fundamentals," former world champion J. R. Capablanca noted that this was the hardest of the basic piece-only endgames to win.</p>

<p>His analysis was that the stronger side can win if it can force the rook away from the king, with double threats of checkmating the king, and forking rook and king. If the defending side can keep the rook near the king without getting checkmated, it can draw. Often, the win or draw is just a matter of a square or two; e.g., the rook's staying on the same or opposite square color as the king (it is easier to fork them in the former case).</p>
 2359: <p>There are several key positions from which it is easy to memorize the win. The basic idea is to drive the opposing king to the edge of the board, and then to the corner, where you can force the rook to separate from the king.</p>

<pre>
<code>
[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "King and Queen"]
[Black "King and Rook"]
[Result "*"]
[SetUp "1"]
[FEN "8/6rk/5K2/3Q4/8/8/8/8 w - - 0 0"]
[PlyCount "11"]

1. Qh1+ (1. Qh5+? Kg8 {this is the diagram we want, but the wrong side has the
move.}) 1... Kg8 2. Qh5 {This is the key position to have with black to move.
The rook must leave the king} Rg1 (2... Kf8? 3.Qh6) 3. Qd5+ Kh7 4. Qe4+ Kg8 5. Qa8+ Kh7 6. Qa7+ {
forks the king and rook} *

</code>
</pre>

<p>The first move in the diagram is Qh1+. Qh5+? is a mistake, though the position is the one we want the wrong side is to move.</p>

<p>After 2.Qh5 we have the position we want. The rook must leave the protection of the king, and a series of checks will allow a fork of king and rook by the queen.</p>

<p>If the rook is already separated, then there is usually a sequence of checks that produce the win.</p>

<pre>
<code>
[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "King and Queen"]
[Black "King and Rook"]
[Result "*"]
[SetUp "1"]
[FEN "8/8/8/4K3/r6k/8/3Q4/8 w - - 0 3"]
[PlyCount "9"]

3. Kf5 Kg3 4. Qd3+ Kh4 5. Qc2 Ra5+ 6. Kf4 Kh3 7. Qc3+ *

</code>
</pre>
 2042: <hr />
<h2><em>INTRODUCTORY NOTE:</em></h2>
<p>Examples and instructions are taken from the book:</p>
<p>Y.Averbakh - Comprehensive Chess Endings Volume 3.</p>
<p>In many cases I felt no need to &quot;reinvent the wheel&quot; so I quoted the above authors. Those parts will be marked with apostrophes <code>&quot;&quot;</code>, like this: &quot;This is a quoted text&quot;.</p>
<hr />
<p>Without further delay let us tackle this endgame:</p>
<p>&quot;In endings of this group the stronger side normally wins thanks to its big material advantage. At the same time, in a number of positions the rook's fighting quality enables it to put up a successful defense. <strong>Drawing dangers arise each time that the weaker side's  king, on being pushed to the edge of the board, becomes restricted in its mobility</strong>&quot;-emphasis are mine.</p>
<p>So let us first start with the position in which rook can successfully defend.</p>
<pre><code>[Title &quot;Weaker side holds balance: Ponziani, 1782&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;5k2/6r1/4Q3/8/8/8/8/7K b - - 0 1&quot;]

1...Rh7+ 2.Kg2 Rg7+ 3.Kf3 Rf7+ 4.Kg4 Rg7+ 5.Kf5 Rf7+ 6.Kg6 Rg7+ 7.Kh6 Rh7+! 8.Kxh7 1/2-1/2
</code></pre>
<p>Here is another relevant position:</p>
<pre><code>[Title &quot;Weaker side holds balance: Berger, 1889&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;6k1/6r1/5Q2/8/8/8/8/7K b - - 0 1&quot;]

1...Rh7+ 2.Kg2 Rg7+ 3.Kh3 Rh7+ 4.Kg4 Rg7+ 5.Kh5 Rh7+ 6. Kg5 ( 6.Kg6 Rh6+! 7.Kxh6= ) 6...Rg7+ 7.Kh6 Rh7+ 8.Kg6 Rh6+! 9.Kxh6 1/2-1/2
</code></pre>
<p>Another important note from the authors:</p>
<p>&quot;If, for example, the queen is moved to <code>f1</code>,<code>f2</code>,<code>f3</code> or <code>f4</code>, the game ends in a perpetual check, since the king can not cross the <code>f-file</code>. But <strong>with his queen at <code>f5</code> White wins: when his king occupies the <code>h6</code> the rook does not have a saving check on <code>h7</code>.</strong>&quot;</p>
<p>Let us move on to another important position, and again I will quote the authors:</p>
<p>&quot;If the queen is stalemating the king in the corner of the board, the rook may become a <em>desperado</em>.&quot;</p>
<p>The following example shows a badly posted rook trying to save the game in this manner.</p>
<pre><code>[Title &quot;Failed 'desperado' attempt&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;r6k/5Q2/2K5/8/8/8/8/8 b - - 0 1&quot;]

1...Ra6+ 2.Kc5 Ra5+ ( 2...Rc6+ 3.Kd4 Rd6+ 4.Ke5+- ) 3.Kd4 Ra4+ 4.Kc3 Ra3+ 5.Kb2+-
</code></pre>
<p>Stronger side should maneuver with its king so that one of the checking squares is covered with the queen-this way queen can take the rook which frees opposing king from stalemate. King should approach the rook <strong>along a diagonal adjacent to the queen's.</strong></p>
<p>Now let us see how weaker side defends when rook is properly posted:</p>
<pre><code>[Title &quot;Drawn for any position of the White king!&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;7k/5Q2/2K5/8/8/8/8/r7 b - - 0 1&quot;]

1...Rc1+ 2.Kd5 ( 2.Kd6 Rd1+ 3.Ke6 Re1+ 4.Kd7 Rd1+ 5.Ke8 Rd8+! ( 5...Re1+?? 6.Kf8+- ) 6.Ke7 Rd7+ 7.Kxd7=) 2...Rd1+! ( 2...Rc5+?? 3.Kd4+- ) 3.Kc5 Rc1+ 4.Kb4 Rb1+ 5.Ka3 Ra1+ 6.Kb2 Rb1+ 7.Kc2 Rc1+=
</code></pre>
<p>Perpetual check! Do not forget that in this position <strong>rook must never leave the first rank!</strong> See the sub variation for the second Black's move ( <code>2...Rc5+?? 3.Kd4+-</code> ).</p>
<p>Now let us move the rook on the <code>g-file</code>:</p>
<p><strong>Do not forget that here rook must not leave the <code>g-file</code>!!</strong></p>
<pre><code>[Title &quot;Drawn for any position of the White king!&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;6rk/5Q2/8/8/8/2K/8/8 b - - 0 1&quot;]

1...Rg3+ 2.Kd4 Rg4+ 3.Ke5 Rg5+ 4.Ke6 ( 4.Kf6 Rf5+!= ) ( 4.Kd6 Rg6+= ) 4...Rg6+! 1/2-1/2
</code></pre>
<p>Let us sum up: <em>In these types of positions the defender draws if his rook operates along the <code>g-file</code> or the <code>1st rank</code>. Of course, this also applies for all 8 mirror positions.</em></p>
<p>For further details of playing these positions refer to the above book. In normal situations the queen always wins against a rook, although not without overcoming certain technical difficulties.</p>
<p>&quot;The winning plan consists of pushing the opponent's king into the corner or onto the edge of the board and creating mating threats. In defending, the weaker side is forced to separate his forces, which leads to the loss of the rook by coming under double attack by the queen. The basic method of achieving the goal is zugzwang.&quot;</p>
<pre><code>[Title &quot;Stronger side wins: Philidor position&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;1k6/1r6/2K5/Q7/8/8/8/8 b - - 0 1&quot;]

1...Rh7 ( 1...Rb1 2.Qd8+ Ka7 3.Qd4+ Ka8 4.Qh8+ Rb8 ( 4...Ka7 5.Qh7+ Ka8 6.Qxb1+- ) 5.Qa1# )  ) 2.Qe5+ Ka8 3.Qa1+! Kb8 4.Qb1+ Ka8 5.Qxh7+- 
</code></pre>
<p>If stronger side is to move, <strong>it gives back the move to the weaker side with the following maneuver:</strong></p>
<pre><code>[Title &quot;Stronger side wins: Philidor position&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;1k6/1r6/2K5/Q7/8/8/8/8 w - - 0 1&quot;]

1.Qe5+ Ka8 2.Qa1+! Kb8 ( 2...Ra7 3.Qh8# ) 3.Qa5+-
</code></pre>
<p><strong>This maneuver is characteristic for this endgame.</strong></p>
<p>The authors continue with practical examples of driving the weaker side's king to the edge/corner of the board <strong>but give no written instructions</strong> on how to achieve this.</p>
<p>This is not satisfactory for my standards thus I have tried to find a better resource for this. I believe <a href="https://rolandbesblogs.com/chess-endings.html" rel="nofollow noreferrer">this</a> is decent coverage for the plan of pushing weaker side's king to the edge/corner of the board. Just look articles for second and third rank defense. If I find anything better I will edit my post, but for now this is the best I can find.</p>
<p>Best regards.</p>
