They have played 30 times in their career, with Djokovic winning 21 of the matches. More significantly, Djokovic has played Murray three times in the Australian Open final and won each time, including last year. Murray also played Roger Federer for this championship as well -- and lost that match, too.
Now Murray will play for the Australian Open a fifth time Sunday, looking to become the first man in the Open era to win a Grand Slam after losing in the finals at that same event four times. He also is trying to avoid becoming the second man in the Open era to lose five Grand Slam finals at one event. (Ivan Lendl is the only other one.)
But he has to beat Djokovic to finally win here.
"Five finals is a great achievement," Murray said. "You can't take that away from me. I should be happy about that. There are very few players that will have made five Australian Open finals, so I have to be proud of that achievement. Obviously when you get to the final you're disappointed if you don't win. But I've obviously played very good tennis here.''
After coming off a very long 2015 season that ended with a Davis Cup victory in late November, Murray has had a lot to deal with emotionally this tournament. His wife is back home, so close to delivery of their first child that Murray said he would abandon the tournament if she went into labor early -- even if it meant withdrawing from the final.
Worse, his father-in-law, Nigel Sears, collapsed at Rod Laver Arena and had to be rushed to the hospital on Jan. 23 while Murray was playing on Margaret Court. Sears recovered but had he not, Murray said he would have withdrawn for that reason as well.
In addition to that, he had to rally to beat Milos Raonic in a draining four-hour, five-set semifinal match Friday while Djokovic played Federer in a 2:19 semifinal Thursday that was among the best match he's ever played. That means Murray goes into Sunday with one day of rest compared to two days for Djokovic.
"Obviously if you play the five sets it isn't ideal,'' Murray said, "but Novak also won here the time we played five hours and then played a six-hour final. So it's doable.''
Djokovic and Murray are the two top-ranked players in the world, but Novak's point total is nearly double that of Andy's. Murray also has lost 10 of their past 11 meetings over the past two seasons, with his only victory in that span at last year's Rogers Cup. And he's 0-4 against Djokovic here, including the 2012 semifinal.
"It's no secret we know how we play against each other,'' Djokovic said. "It's two games that are very much alike, so it's basically who's going to outplay who from the baseline. I think serve is an important factor in tomorrow's match. I think both of us will try to serve a high percentage of first serves and not allow the other player attack the second serve too many times.
"As I said, we have very similar styles of game and very similar trajectory to the professional tennis, so it's nice to see that our rivalry keeps on going and we keep playing for the biggest titles.''
But Murray sees progress.
"Last year here is a good match for me to look at because the tennis, in my opinion, wasn't miles apart. It was a very close match for three sets,'' Murray said. "The most important thing for me is to sustain my level for long enough, not just for one set here or there, a few games here or there. I need to do it for a very long period if I want to get the win. That's my challenge on Sunday.''
Can he meet the challenge? The odds are against him, as they usually are when he plays Djokovic. But he has beaten his longtime rival often enough -- he is 6-7 against him in Tour-level finals -- to stand a decent chance to finally hold the trophy, in addition to holding his soon-to-arrive child.
"I have a very good shot on Sunday if I play my best tennis," Murray said. "I need to do it for long enough to have a chance. I'm aware of that. I don't think many people are expecting me to win on Sunday. I have to just believe in myself, have a solid game plan, and hopefully execute it and play well.''