Ai-Thinker ESP8266 Wi-Fi Module ESP-12S 4MB

This ESP-12S is an improved model with respect to the ESP-12F module, but is not a direct replacement in connection with the missing pins at the bottom of the module. Since these pins are not used in most cases, it is in most cases a replacement for the ESP-12F (or other module from the ESP-12 series)
The ESP-12S has improvements in PCB design for better Wi-Fi stability and anti-interference.

This module offers you the possibility to connect your Arduino to Wi-Fi for a very low price.

The ESP8266 module works with the normal UART port on your Arduino and can connect to networks, form your own network (hot spot) or both. The possibilities with this module are endless!

If you want to make a start (in Dutch), look here. In addition, you can find enough information at SeeedStudio, Instructables - ESP8266 Wi-Fi Temperature Logger, ESP8266 forum,Hackaday and Nurdspace.
The module can also receive an update (more functionality, more stable, etc.). These sites have good descriptions:   ESP8266: Reflash Dance! and BikeAlive.

This variant has 4MB memory and must be soldered.

This datasheet contains more specific information if needed.

Note: This module may be delivered without a pre-programmed firmware!