With my iPhone 4 I started using the Atomic Floyd SAF0106/01/00 AirJax +Remote Earhook Stereo Headset and continued in doing so when I switched to the Lumia 1520 without a hitch.
Somewhere down the road one of the Ear Buds started acting up so I sent them back for a replacement and received the Atomic Floyd SAF0108/05/00 AirJax +Remote Earhook Stereo Headset which, on first look, is basically the same thing with just a different colored/material cable - Didn't work with my Lumia 1520 as I was neither able to start/stop Music nor receive/cancel Calls.
Had to send it back again and ask for the first revision model - They managed find one of the last remaining Atomic Floyd SAF0106/01/00 AirJax +Remote Earhook Stereo Headset somewhere in a storage and sent me that one - With that in mind I immediately got myself a 2nd one from Amazon, which right now is just lying around.