The competition at this event is quite intense, and winning this tournament can give players a real confidence boost going into the new year.
Let's look at some updates and results from the best players at the ATP World Tour Finals.
Federer is now the No. 2-ranked player in the world, and he has started this tournament in fine fashion with a victory over Janko Tipsarevic in his first match.
Both men are in Group B, and Federer won the match rather easily in straight sets 6-3, 6-1. Federer is the favorite to finish first in this group, which also includes Juan Martin del Potro of Argentina and David Ferrer of Spain.
This is a tournament that Federer knows very well and has won six times, most recently last year.
Fans are hoping that Federer squares off against Novak Djokovic and/or Andy Murray at some point in this tournament, but both of these men will have to survive in Group A first.
The Serbian star will play Andy Murray on Wednesday in what will be the best and most competitive matchup in the early stages of the tournament.
Djokovic defeated Frenchman Jo-Wilfried Tsonga in both players' first match of the 2012 ATP World Tour Finals.
After winning just one Grand Slam tournament this year (Australian Open in January), expect Djokovic to be motivated throughout this event as he looks to close 2012 on a high note.
He won this tournament in 2008, and hasn't played in the final of the ATP World Tour Finals since that year.
Will Murray win the ATP World Tour Finals?
The reigning Olympic champion has also started his pursuit of an ATP World Tour Finals with an important victory.
He defeated Tomas Berdych of the Czech Republic, who has been one of the best players not named Djokovic, Murray, Federer or Nadal this season.
Winning this tournament would be the perfect way for Murray to end a memorable season. If he can beat Djokovic on Wednesday, he will have a great chance to reach the semifinals in London.