Details have emerged on how the PlayStation 4 will handle backwards compatibility for last-gen headsets.
First off, if your headset relies on Bluetooth for chat, your headset won't work at all with the PS4. This is the most devastating of the news, Sony did not give a reason why, but this is how it will be.
Now, if you're headset uses USB for chat (such as the Astro A50) an update will eventually be available so you can use your headset. This also applies for the Sony branded PULSE headsets (and the Elite edition).
Headsets that use digital optical for game audio will still work, however you will need to wait for the patch to chat.
The only headsets that will work 100% on day one will be the Turtle Beach XP510, PX51, the new PX4 model that launches November 15th, and obviously the mono headset included with the PS4.