Depends on what you mean by "very low consumption". For one project I used a SparkFun SAMD21 Mini Breakout[0], and with the RTCZero[1] library was pretty easily able to get it down to 0.3mA when sleeping and averaging 1.3mA overall. (OK, I had to desolder the power LED which was eating 3mA.) I've since switched over to using Adafruit Feather M0 boards for most stuff, which is basically the same thing.

[0] https://www.sparkfun.com/products/13664 [1] https://www.arduino.cc/en/Reference/RTC

edit: Oh sorry I missed the "with wifi" in your post. One nice thing about the ESP8266 is that lots of people use it -- hopefully that means you can find details on how to run it in low power modes.