Facetime says connecting, but won't connect.

All of a sudden my facetime is not working on all of my devices (iPad 2, iPhone 5c, iPhone 4s) on either wifi or cellular. These have worked perfectly for months, but today none will connect with each other or any other facetime user. I've tried turning facetime on and off, rebooting all of the devices, but to no avail. It's not wifi, because the problem is with cellular as well.

I presume that the issue must be related to my user id, but I've checked passwords etc. are correct. Any ideas how to fix this?