From their FAQ:
YouTube TV is a TV streaming service that lets you watch live TV from major broadcast and popular cable networks. Enjoy local and national live sports, and must-see shows the moment they air. Record all your favorites without storage space limits, and stream wherever you go. Share with up to 5 other roommates or family members in your household.
and
You can record as many programs as you want at the same time, without ever running out of storage space. We’ll even keep each recording for 9 months. Stream from your library anywhere in the U.S.
They say they even let you fast forward through commercials on programs you've recorded.