Rapid and blitz chess are fast chess games that range from a couple of minutes per game to less than an hour. In the World Championships the top players in the world will play 3 days of rapid chess and two days of blitz chess.
In rapid chess each player has 15 minutes per game and gets an additional 10 seconds per move. They play 5 matches a day. In blitz chess each player has 3 minutes per game and gets an additional 2 seconds per move. They play 10 matches a day. There is a separate champion for each format.
Current ranking of tournament can be found at the Official Website.