user23168: In my work, I have an ESP-8266, Arduino-Uno and a Relay. ESP 8266 and Uno is connected. Relay's data signal is take from arduino's 12th pin. ESP is powered from Uno.
If I use two different power sources for Uno and Relay, Relay does not response for the signal from Uno. (Both have a same common ground)
If relay is powered from Uno, then after load control (power on and off) ESP-8266 goes down.

user15165: Use  a relay driver IC like ULN2003 to drive relay. 
Here is a sample circuit diagram : 

user10394: The uno can't provide enough power to power an ESP8266 reliably.  I suggest you power it from a separate source.
When ever you use separate power supplies for a circuit you need to "tie the grounds together", connect them.  Otherwise the circuits don't use the same definition of zero.  

23168: <p>In my work, I have an ESP-8266, Arduino-Uno and a Relay. ESP 8266 and Uno is connected. Relay's data signal is take from arduino's 12th pin. ESP is powered from Uno.</p>

<p>If I use two different power sources for Uno and Relay, Relay does not response for the signal from Uno. (Both have a same common ground)</p>

<p>If relay is powered from Uno, then after load control (power on and off) ESP-8266 goes down.</p>
 15165: <p>Use  a relay driver IC like ULN2003 to drive relay. 
Here is a sample circuit diagram : <a href="https://i.stack.imgur.com/b0ZBt.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/b0ZBt.png" alt="enter image description here"></a></p>
 10394: <p>The uno can't provide enough power to power an ESP8266 <strong>reliably</strong>.  I suggest you power it from a separate source.</p>

<p>When ever you use separate power supplies for a circuit you need to "tie the grounds together", connect them.  Otherwise the circuits don't use the same definition of zero.  </p>
