White will mate after ...Kc8 Qxb7# or ...Ke8 Qf7#.
Checkmate Question
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It's very rare to find a grandmaster game that goes all the way to checkmate. Most often one side resigns when the position becomes hopeless. That said, it's not uncommon for us non-titled players to reach the end of a game and think "no! there's still hope, play it out!"
In the linked game, white won in that position because black resigned. Black probably realized his position was hopeless a few moves before hand, and was being a bit stubborn forcing his opponent to play a few more correct moves.
I don't understand why checkmate has occurred in this match: http://www.chess.com/games/view.html?id=1080381#
Why can't the king safely move to c8 or e8?