I had been searching on how to run an esp8266 data logger with minimumal power consumption on a 18650 3.7V Li-ion battery and come accross this solution.1
Althought you can minimise the power consuption of an esp8266 with deep sleep, usually you have other sensors/chips that are cosuming power. The idea is to use an Atmel ATtiny13A - Microchip picoPower 8-bit AVR RISC-based microcontroller, it's up and running 24/7 while everything else is without power, so the consumption of the rest of the circuit is 0A. ATtyni13A consumption is only 0.005mA (5µA) in a sleep mode.
As you can see, ATtyni13A is used only as a controller of 1 N-channel MOSFET, that is turning on/off a 3.3V power regulator for the esp8266 and it's sensors.
1: Home Circuits Blog - Low power (5microA) ATtiny13A
avrdude command line with Atmel Studio 7.0 External Tools
Title: USBasp
Command: c:\users\<user>\Documents\Atmel Studio\avrdude-6.3-mingw32\avrdude.exe
Arguments: avrdude -v -pattiny13 -cusbasp -Pusb -U flash:w:"$(ProjectDir)Debug\$(TargetName).hex":i
Use Output Window: True
Title: USBasp fuse
Command: c:\users\<user>\Documents\Atmel Studio\avrdude-6.3-mingw32\avrdude.exe
Arguments: avrdude -v -pattiny13 -cusbasp -Pusb -Ulfuse:w:0x6A:m -Uhfuse:w:0xFF:m -Ulock:w:0xFF:m
Use Output Window: True