It wasn't easy, and he had some good fortune along the way, but Sergey Karjakin's resourcefulness and resilience enabled him to qualify for the finals of the World Cup and for next year's Candidates' tournament by defeating Pavel Eljanov 2.5-1.5 in the tiebreaker. Eljanov, whose overall play in the World Cup was probably the best of all 128 players, came extremely close to qualifying, but one narrow miss after another stopped him just short of the event's ultimate prize.
In the first g/25 Eljanov won an excellent game with the white pieces, but in the rematch Karjakin won an equally impressive win in his white game. Eljanov had more chances to hold than Karjakin, but in both cases the player with White kept up the pressure until his opponent cracked. In the g/10 battles, however, Karjakin saw Dame Fortune smile on him repeatedly. In the first game, Eljanov had a big advantage, but 42.h4? made it equal and 43.h5?? left him lost. Even after that he had a couple of subtle chances to save the game or at least make Karjakin's job a lot tougher, but without time to find these better moves Karjakin reeled in the point. Needing to win with the black pieces to stay alive, Eljanov somehow managed to outplay Karjakin and obtain a winning endgame, but he missed several wins and then stumbled into a threefold repetition. (The games, with my comments, are here.)
A huge pity for Eljanov, but sport can be cruel. Karjakin will meet Peter Svidler in the final, and while there's money and the title at stake both players have achieved their main competitive goal; namely, qualification to next year's Candidates' tournament. The other known candidates are Viswanathan Anand (for making it to the last world championship match), Hikaru Nakamura and Fabiano Caruana (both from the Grand Prix). I think the expected favorites to qualify by having the best average rating in 2015 are Veselin Topalov and Anish Giri, and that will leave one more player to be determined by the organizers of the Candidates' tournament (scheduled for March of 2016). As of this moment, the venue isn't yet known - or at least not publicly known, but standard operating procedure is for the host country (or at least the organizer's/sponsor's host country) to get the pick.
Anyway, that's off in the more distant future. First things first: the final match will be a best-of-four (rather than a best-of-two), to be followed if necessary by the same set of rapid tiebreakers. Tomorrow (today - Wednesday) is a rest day, and the match will begin on Thursday.