Where are the replays
Every game that you take part in will save a replay on your hard drive at C:\ProgramData\FAForever\replays or where you installed your FAF
There is a list of recently played games stored online at http://faforever.com/faf/vault/replays_simple.php
Handy to note, if you move these replays to your replays folder you are then able to launch them from the Replays tab at the bottom of FAF.
Thanks to Valkyria and the dedicated GPGNET staff for releasing and hosting all replays from GPGNET. The can be found here http://vault.gurut.org/search/