user2792: Basically, I would like to ask people to share their knowledge on famous and/or particularly instructive examples of chess positions, which chess engines do not understand well (i.e. do not evaluate correctly).
A good example of the kind of positions I am interested in is the Vančura Position-Wiki (cf. also Vančura Position-Chessbase), which occurred very recently (at the Sinquefield Cup 2014) in the game Carlsen-Aronian. Although the engine was saying white is completely winning, the game was a theoretical draw after black's 48th move.
Thanks in advance!
P.S. I should stress that I am looking for realistic examples, i.e. those which are likely to happen in a real game. Positions of the following type,
[fen "4k3/4p3/3pPp2/2pP1Pp1/1pP3Pp/pP1K3P/P2RRR2/8 w - - 0 1"]

and similar artificial positions is not the kind of thing I am looking for.
I should also say that endgame tablebase examples are OK. The only requirement is that engines (run on an average computer) are not able to evaluate the position correctly after given, say, 10-15 minutes time to "think".

user1485: Besides fortresses, another type of position the engines tend to get wrong is when the weaker side is about to promote a pawn but the promotion can be delayed indefinitely. 
[FEN "5Q2/8/8/8/2k5/7P/1p4PK/r7 w - - 0 1"]
[White "Anatoly Karpov"]
[Black "Anthony Miles"]
[Event " Biel"]
[Date "1990  (analysis, white to move)"]

For a human player it is easy to see that this is a draw, but the engine has to try all the different checks from all possible squares in all different orders. (I haven't tested this position with the newest engines, perhaps some of them can handle this?)

user3456: 1Q2r1k1/P6p/8/8/4q3/7P/6PK/8 w - - 2 6

White to move. 1.a8=Q Qxa8 2.Qg3+ may be a perpetual check that is hard to analyze. See the comments in the discussion of this tactics problem at http://chesstempo.com/chess-problems/103006

user3456: http://chesstempo.com/chess-tactics/90023
The final position of the solution is an ending with queen against two knights with pawns on both sides where the knights can set up a blockade. Looks like a draw but the engine evaluates that the queen side wins.
8/5ppk/7p/3pP3/5P2/5N1P/4NKP1/7q b - - 0 5


user3831: The following two links seem to be exactly what you are looking for (many such positions in each one of them).
http://en.chessbase.com/post/can-we-still-deceive-computers-in-chess
http://www.chess.com/forum/view/general/positions-engines-get-wrong--please-contribute
A cute study, which engines are unable to solve last I checked (white to move and win):
6r1/p1p1p1pP/P1PpP1P1/8/2P1B3/2K3pp/3P2rq/R5bk w - - 1 0


2792: <p>Basically, I would like to ask people to share their knowledge on famous and/or particularly instructive examples of chess positions, which chess engines do not understand well (i.e. do not evaluate correctly).</p>

<p>A good example of the kind of positions I am interested in is the <a href="http://en.wikipedia.org/wiki/Rook_and_pawn_versus_rook_endgame#Van.C4.8Dura_position">Vančura Position-Wiki</a> (cf. also <a href="http://en.chessbase.com/post/karsten-mueller-understanding-the-vancura-draw">Vančura Position-Chessbase</a>), which occurred very recently (at the Sinquefield Cup 2014) in the game <a href="http://www.chessgames.com/perl/chessgame?gid=1772860">Carlsen-Aronian</a>. Although the engine was saying white is completely winning, the game was a theoretical draw after black's 48th move.</p>

<p>Thanks in advance!</p>

<p>P.S. I should stress that I am looking for realistic examples, i.e. those which are likely to happen in a real game. Positions of the following type,</p>

<pre><code>[fen "4k3/4p3/3pPp2/2pP1Pp1/1pP3Pp/pP1K3P/P2RRR2/8 w - - 0 1"]
</code></pre>

<p>and similar artificial positions is <strong>not</strong> the kind of thing I am looking for.</p>

<p>I should also say that endgame tablebase examples are OK. The only requirement is that engines (run on an average computer) are not able to evaluate the position correctly after given, say, 10-15 minutes time to "think".</p>
 1485: <p>Besides fortresses, another type of position the engines tend to get wrong is when the weaker side is about to promote a pawn but the promotion can be delayed indefinitely. </p>

<pre><code>[FEN "5Q2/8/8/8/2k5/7P/1p4PK/r7 w - - 0 1"]
[White "Anatoly Karpov"]
[Black "Anthony Miles"]
[Event " Biel"]
[Date "1990  (analysis, white to move)"]
</code></pre>

<p>For a human player it is easy to see that this is a draw, but the engine has to try all the different checks from all possible squares in all different orders. (I haven't tested this position with the newest engines, perhaps some of them can handle this?)</p>
 3456: <pre><code>1Q2r1k1/P6p/8/8/4q3/7P/6PK/8 w - - 2 6
</code></pre>

<p>White to move. 1.a8=Q Qxa8 2.Qg3+ may be a perpetual check that is hard to analyze. See the comments in the discussion of this tactics problem at <a href="http://chesstempo.com/chess-problems/103006" rel="nofollow">http://chesstempo.com/chess-problems/103006</a></p>
 3456: <p><a href="http://chesstempo.com/chess-tactics/90023" rel="noreferrer">http://chesstempo.com/chess-tactics/90023</a>
The final position of the solution is an ending with queen against two knights with pawns on both sides where the knights can set up a blockade. Looks like a draw but the engine evaluates that the queen side wins.</p>

<pre><code>8/5ppk/7p/3pP3/5P2/5N1P/4NKP1/7q b - - 0 5
</code></pre>
 3831: <p>The following two links seem to be exactly what you are looking for (many such positions in each one of them).</p>

<p><a href="http://en.chessbase.com/post/can-we-still-deceive-computers-in-chess">http://en.chessbase.com/post/can-we-still-deceive-computers-in-chess</a></p>

<p><a href="http://www.chess.com/forum/view/general/positions-engines-get-wrong--please-contribute">http://www.chess.com/forum/view/general/positions-engines-get-wrong--please-contribute</a></p>

<p>A cute study, which engines are unable to solve last I checked (white to move and win):</p>

<pre><code>6r1/p1p1p1pP/P1PpP1P1/8/2P1B3/2K3pp/3P2rq/R5bk w - - 1 0
</code></pre>
