The two have met 20 times, with Murray winning 12 of those matches.
Most recently, Murray has beaten Federer in the gold-medal game of the 2012 Summer Olympics and in the semifinals of the 2013 Australian Open.
While Murray is one of only two active players—Rafael Nadal being the other—to have a winning record against Federer, he has figured out one of the secrets to beating Federer.
That secret lies in a low error rate. Not only does Murray not make a lot of errors, he forces his opponent into making mistakes.
In their Australian Open clash, Murray made only eight errors in the fourth set, as opposed to 11 by Federer, according to the BBC.
In total, Murray had 15 more winners than unforced errors, according to Sports Illustrated.
This is not new for Murray. An analysis by the Wall Street Journal suggests that Murray's risk-adverse play is a part of his success.
In 2011, according to the analysis, Murray hit 36 percent fewer unforced errors than his opponent. In 2012, that number dropped to 21 percent, but is still significantly better than his counterparts.
Murray's risk-adverse style does not make for a particularly exciting brand of tennis, but it keeps him in the game longer than those who try to take chances and catch Federer out of position.
Because Federer is so sound, both in technique and positioning, it's hard to catch him out of place. It's hard to force him into a bad shot. The only way to beat him is to make as little mistakes as possible.
That's what Murray does and that's what he excels at. The less mistakes Murray makes, the longer he stays in the game.
When he combines his low error rate with a phenomenal serve, it's tough for anybody—even Roger Federer—to beat him.
Going forward, other players will study Murray's game to get insight on what it takes to beat the legendary Federer. They'll notice the low errors and they'll try to adapt to that risk-adverse style.
It's really the only way to beat Federer. Murray knows the tricks and he's showing us on a pretty regular basis.
Federer is still great, and a few losses to Murray does not mean that he's lost his touch.
What it does mean is that the ways to beat him are becoming clear, and the players who can exploit that will have the most success.
Murray knows just how to exploit Federer. He knows that not taking too many chances is the only way to beat Federer.
From now on, Federer will have to adapt to the waves of players trying to emulate Murray.
If he can, it'll add to his remarkable legacy that makes him one of the greatest tennis players to ever play. A reinvention is almost as impressive as the original.
If not, he'll still be great, but the frequency with which he wins will decrease.