Federer was in action early on and coasted to victory against Steve Johnson in straight sets. Djokovic didn't have things quite so easy against Jan-Lennard Struff, although he was eventually able to outlast his opponent over the course of four sets.
In the women's draw, defending champion Naomi Osaka and seven-time winner Serena Williams both progressed with routine victories. There was also a win for 15-year-old Coco Gauff, who again got the better of veteran Venus Williams in the opening round of a Grand Slam.
Here is a look back at some of the main highlights from Day 1, with some of the greats of the game gracing the court in Melbourne.
Australian Open - Round 1, Selected Results
(2) Novak Djokovic bt. Jan-Lennard Struff: 7-6 (5), 6-2, 2-6, 6-1
(3) Roger Federer bt. Steve Johnson: 6-3, 6-2, 6-2
(6) Stefanos Tsitsipas bt. Salvatore Caruso: 6-0, 6-2, 6-3
(8) Matteo Berrettini bt. Andrew Harris: 6-3, 6-1, 6-3
Marton Fucsovics bt. (13) Denis Shapovalov: 6-3, 6-7 (7), 6-1, 7-6 (3)
(1) Ashleigh Barty bt. Lesia Tsurenko: 5-7, 6-1, 6-1
(7) Petra Kvitova bt. Katerina Siniakova: 6-1, 6-0
(8) Serena Williams bt. Anastasia Potapova: 6-0, 6-3
(13) Petra Martic bt. Christine McHale: 6-3, 6-0
(14) Sofia Kenin bt. Martina Trevisan: 6-2, 6-4
For Monday's results in full, visit the Australian Open website.
Federer looked in excellent shape on Monday, and he began his quest for a 21st Grand Slam title in style.
The Swiss was dynamic and ruthless against Johnson, quickly stamping his authority on the game and moving through the gears.
Per Jose Morgado of Record, Federer commented on how long he's been at the top of the game for after his routine victory:
Djokovic, who is the defending champion and seeking an eighth win at this event, is expected to be one of Federer's main rivals for the title down under.
Although he was able to make it into the second round, there were signs of vulnerability from the Serb against Struff, particularly in an error-prone and erratic third set.
Per The Tennis Podcast, it's been a long time since Djokovic surrendered a set at such an early stage of the Australian Open:
The champion will at least be encouraged by the way he played in the fourth set, in which he was able to up his levels and ensure any faint hopes Struff had of a comeback were quickly dashed.
Elsewhere, there were no problems for Osaka or Serena Williams in their opening matches, with each picking up expected comfortable wins.
Per Eleanor Crooks of the Press Association, there was a steely focus about Serena as she overcame Potapova:
The most anticipated match of the day was between Gauff and Venus Williams, with the two meeting in a Grand Slam first round for the second time after their Wimbledon tussle last year.
Once again, it was the youngster who was able to prevail against her senior opponent, winning 7-6 (5), 6-3.
Afterward, Christopher Clarey of the New York Times paid tribute to both players:
Christopher Clarey @christophclarey
Coco Gauff is 2-0 against Venus Williams. beats her 7-6 (5), 6-3 in the first round of the Australian Open after beating her in the first round of Wimbledon last year. At 15, Gauff has a big career in front of her. At 39, Venus is love of the game and the fight personified.
The WTA Insider Twitter account put this latest success by the teenager into some context:
WTA Insider @WTA_insider
Most Slam MD wins before turning 16: CAPRIATI: 28 (90-92) HINGIS: 20 (95-96) RINALDI: 13 (81-82) GRAF: 12 (83-85) MJ FERNANDEZ: 11 (85-87) SELES: 11 (89) SABATINI: 9 (84-85) MAGDALENA MALEEVA: 6 (90-91) MANUELA MALEEVA-FRAGNIERE 6 (82) *GAUFF: 6 (19-20)* KARATANTCHEVA: 5 (04-05)
There was a scare for the home favourite and top seed on Monday, too, when Ashleigh Barty fell a set down against Tsurenko.
However, the French Open champion was able to rally back and only dropped two more games in the match, much to the delight of the Melbourne crowd.