The Xbox 360 ruled most of last gen and that might of gone to Microsoft's head. The One has several issues and one is the lack of headphones. There is an adapter in the works that will allow you to use current Turtle Beach and I'm assuming Astro headphones with the One but that will not come out to sometime between March and June. You might be thinking Microsoft is trying to get you to buy new headphone except there are none.
Two sets of Turtle Beach headphones are listed on Xbox One's accessory page however when you go to Turtle Beaches website it says coming soon. If you go to Astro's website the One isn't even listed under platforms. This is all because Microsoft decided to make their own adaptor instead of using USB or a headphone jack.
Microsoft's answer is to use your Kinect as your mic and while this works ok I do some late night gaming and don't want to wake anyone up in my house because I'm trying to talk loud enough to get the Kinect to hear me. To make matter worse the PS4 works with Turtle Beach headsets with a $6 cord or you can use almost any headphones by plugging them into the controller.