The ESP8266 is a chip that turned a lot of heads recently, stuffing a WiFi radio, TCP/IP stack, and all the required bits to get a microcontroller on the Internet into a tiny, $5 module.
So you design in an external ADC chip and connect it via I2C, or you tack on a shift register and drive it with the blindingly fast I2S peripheral — something you can’t do with the ESP8266.