ESP8266
The ESP8266 is a WiFi-enabled SOC (system on chip) which can run open-source firmware, such as nodeMCU (an eLua interpreter), Ai-Thinker (a simple TCP/IP stack to act as a serial-to-TCP WiFi adapter), a bootloader to use with the ArduinoIDE or any other program written with the SDK (software development kit).
The ESP8266 chip can be readily purchased, presoldered on a small PCB module with different pins broken out for easy access.
Modules
E-01
The E-01 module is of the cheapest and simplest modules with only 8 pins broken out to a 2x4 pin header. Since this module is not very breadboard friendly with the 8x2 pin header, we have a special E-01 USB flashing tool at the commons|lab.
E-12
This module is FCC-licensed and has more pins of the EAP8266 broken out. The spacing if the pins is not the usual DIP/breadboard spacing of 0.1 inch.
USB-Enabled boards
Amica
The NodeMCU Amica board has the E-12 module and a micro USB port on board.