Rafael Nadal beats Victor Estrella Burgos 6-1 6-1 6-1
GB's Edmund beats Anderson 6-7 (4-7) 6-3 3-6 6-3 6-4
Venus Williams & US Open champion Stephens knocked out
Seeds Wozniacki & Svitolina through in women's event
Kyrgios wins his opening match in straight sets
Australia's Daria Gavrilova beats Irina Falconi 6-1 6-1
Up next on Rod Laver, is Daria Gavrilova - the Russian-born 23-year-old who switched allegiances to Australia in 2015.
She plays in front of a home crowd against Irina Falconi of the USA. You can listen to that match on BBC Radio 5 live sports extra by clicking on the icon at the top of this page.
Elina Svitolina, the fourth seed in the women's draw, has sailed through to the second round with a 6-3 6-2 win over Ivana Jorovic of Serbia.
And as we mentioned earlier, end-of-season champion Caroline Wozniacki beat Mihaela Buzarnescu in straight sets, while Australian Nick Kyrgios cruised through in 87 minutes against Brazilian Rogerio Dutra Silva.
Nadal 6-1 6-1 6-1 Estrella Burgos
Rafael Nadal will play Leonardo Mayer in the next round, after the Argentinian world number 52 beat Nicolas Jarry of Chile 6-2 7-6 (7-1) 6-3.
Nadal says of Mayer, who he's beaten in all four previous meetings: "We've met couple of times now - the last time in the US open third or fourth round. I need to be ready to compete well from the beginning."
Nadal 6-1 6-1 6-1 Estrella Burgos
Rafa Nadal is asked what he did to recover in time for the first Grand Slam of the season: "I worked. I took a bit of time off as well. I had to stop after London and then take it step by step. I started slower than usual, to do things the right way. I'm so happy to be back with a good start.
How long does he see himself going on for? “This year we are here,” he laughs. “That's all I can say. I love this sport, this competition, One day I won't have the chance to play here again and I don't want to think about how many years I've got left. I just want to enjoy it.”
Nadal 6-1 6-1 6-1 Estrella Burgos
Rafa Nadal speaking on court: "It was a long season in 2017 and I was disappointed to not make it in Brisbane. I just needed more time. I’m happy to be here again. It’s a special unique place and one of the best atmospheres on the tour. To be in front of this crowd is so special."
Nadal 6-1 6-1 6-1 Estrella Burgos
Ruthless.
In one hour and 34 minutes, Rafael Nadal has brushed past Victor Estrella Burgos without really breaking a sweat (bar that ridiculous 14-minute game in the second set).
The pair embrace at the net and share a laugh and a joke. The Dominican 37-year-old gets a huge cheer from the Rod Laver Arena as he walks off, with a broad smile across his face.
*Nadal 6-1 6-1 5-1 Estrella Burgos
Is a bagel on the menu? Not today, thank you.
Nadal shanks a return as Estrella Burgos gets off the mark in his service game and the Dominican overpowers his opponent with a blistering forehand, followed by a big serve, for 40-0.
The 37-year-old fails to hold to love after clipping into the net, and he's then outdone by a straight forehand winner from Nadal.
A gorgeous pick-up volley hands Estrella Burgos the game!
Nadal 6-1 6-1 5-0 Estrella Burgos*
All aboard the Rafael Nadal express.
The next stop: Australian Open second round.
Oh hey, Will Ferrell!
Image source, Getty Images*Nadal 6-1 6-1 4-0 Estrella Burgos
Just when you think Victor Estrella Burgos is about to stop Nadal from racing further ahead, he's off again - full steam ahead.
The Dominican looks solid with a 40-15 lead - until Rafa curls a spinning forehand into the corner.
And then he finds the corner again with a nifty approach shot. Deuce.
Nadal takes the advantage with a brilliant forehand and secures yet another break.
Piers Newbery
BBC Sport at Melbourne Park
Nick Kyrgios notches a straightforward opening win, 6-1 6-2 6-4 against Brazilian Rogerio Dutra Silva. The Australian loves playing on Hisense Arena, the third show court in Melbourne which also doubles as a velodrome when the tennis seating is removed, and there's every chance he will be back here for his next match.
Scheduling is up to the tournament, obviously, but Kyrgios has made it pretty clear this is where he wants to be. Serbia's Viktor Troicki is the next in line.
Nadal 6-1 6-1 3-0 Estrella Burgos*
Nadal pulls out a volley and an overhead smash for 30-0.
Estrella Burgos goes long and the Spaniard holds to love with a backhand winner.
That's 12 consecutive points for the 16-time Grand Slam champion. Brutal.
*Nadal 6-1 6-1 2-0 Estrella Burgos
We're back to it being one-way traffic again.
Estrella Burgos is 0-40 down and another unforced error sees Nadal break with ease.
This could be over very soon.
Was the flexing arm emoji based on Rafael Nadal's left gun?
Image source, Getty ImagesNadal 6-1 6-1 1-0 Estrella Burgos*
Rafael Nadal starts as he means to go on.
A simple hold to get him off the mark in the third set, dropping a solitary point along the way.
Image source, ReutersSecond seed Caroline Wozniacki is safely through to the second round with a 6-3 6-2 victory over Romania's Mihaela Buzarnescu.
The Dane has yet to win a Grand Slam title but is strongly fancied to end that this year in what is a wide-open women's field.
Good start so far.
Image source, Reuters*Nadal 6-1 6-1 Estrella Burgos
This is brilliant entertainment. Estrella Burgos is fired up, slipping and sliding across the court as he attempts to claw something back from this contest against the world's best male player.
After nearly doing the splits, he hands Nadal a break and set point.
And the Spaniard takes it on a replayed point. All that huff and puff for nothing.
Leon Smith
GB Davis Cup captain on BBC Radio 5 live sports extra
Image source, EPAGood on him! Estrella Burgos was getting destroyed but he's hanging in there. He hasn't let his efforts drop, and he's been fighting and fighting. But how hard has he had to fight to win a solitary game!
Nadal 6-1 5-1 Estrella Burgos*
Alleluia!
The biggest roar of the day goes to Victor Estrella Burgos, as he hits a forehand winner past the world number one to finally break him on the sixth attempt.
The Dominican celebrates like he's won the title!
