Arduino has a library for quickly and easily setting up a simple web server on an ESP8622-based board, and [Tomaž] found that power consumption on an ESP-01 can be reduced a considerable amount ...

Peter Lubbers makes an introduction to HTML5 Web Sockets explaining how they interact with proxy servers, and what proxy configuration or updates are needed for the Web Sockets traffic to go through.

The web server firmware opens up a ton of possibilities with CGI scripting. When booting up in AP mode, you can even connect the ESP8266 to another access point right from the your browser.