Arduino and ESP8266 communication over wifi I need to same advice, how to realize communication between ESP and arduino over wifi. I have connected temperature and pressure sensor to ESP, and I need to get this data from sensor to arduino. ESP will be connected to battery, so it should be also low power solution. I thought about something like every 2 minutes read the data and send to arduino, and then deepsleep. However I don’t know, how to realize that communication. I need webserver on arduino and client at ESP? Could someone help me?
On the Uno with Ethernet shield you start an EthernetServer on port 23 or 2323. See ChatServer example.

On esp8266 you create a WiFiClient, connect it to IP address of the EthernetShield and port 23 (or 2323). Everything you print to WiFiClient will be send to EthernetServer's EthernetClient. 

You can test the server with Telnet client.