How does the voice chat work?

Have you enabled it in the options menus (it's off by defualt)?

 I have enabled it. I enabled it to use my headset and mic built into the headset. It all works in The Run and other games but not Rivals.

I'm not sure what platform you're on but on Xbox 360 voice chat normally works for a few minutes, then drops out until you join another session. Luckily we have Party Chat :-)