WARNING: ANY PROJECT THAT USES LITHIUM BATTERIES MAY RESULT IN FIRE OR OTHER BAD THINGS. USE THESE INSTRUCTIONS AT YOUR OWN RISK.
This is a minimal parts, minimal cost battery powered Pi Zero. All you need is a Pi Zero with SD card, a new or used LiIon or LiPo cell, a battery protection board (often part of the cell, or it can be salvaged), a 1K resistor, and some bits of wire. You can tart things up a bit by adding a power on push button, an on-board charger, and voltage monitoring.
All is not perfect, of course - the Pi Zero USB port won't provide 5 volts, just the raw battery voltage. Consequently, some USB devices won't work. But the ones that run on 3.3V internally will work just fine!