The system is meant to be runnable from either a rechargable (3.7V LiPo) battery, or from the USB connection. Ideally (since the WiFi might draw power faster than the battery can be charged), power should come from the USB connection when available, with any spare power being used to recharge the battery. The term here is "load sharing." My favorite chip for this is the MCP 73871. Small, inexpensive, and packed with features, this was a step up for me from the MCP 73831, which is a bit easier to use (and easier for me to solder!) but doesn't do automatic load sharing.

This video talks about the issues I ran into with the 73871 and how I found/fixed the problems. Also shows off the EPS-01 WiFi interface to the board :)