It runs at 80MHz and has 32KBytes of instruction RAM, 96KBytes of data RAM and 64KBytes boot ROM.
It has a RISC architecture and the core is a 106micro Diamond Standard core (LX3) made by Tensilica and is produced by Espressif.
Specs from the producer site:
The chip from the above picture is the old version. The new one is ESP8266EX that is now on all boards that I've seen for sales.
ESP8266Ex is connected on most boards to a SPI flash memory like in the following schematic: