From following the steps in the official apple support page, it seems my computer is not able to recognize my iphone.
Other similar questions show an "unknown device" of some sort, which in my case isn't there. The phone is charging, so it's somehow connected and the USB port works with my mouse for example.
I've tried what's mentioned here but it didn't work. Latest itunes version: 220.127.116.11 Latest IOS version: 9.3.2
EDIT After connecting an ipad, the connection worked via itunes.