Rafael Nadal wins in straight sets 6-3 6-4 6-2 to reach semi-finals
Second seed plays Stefanos Tsitsipas next, who beat Roberto Bautista Agut in four sets
Petra Kvitova beat home favourite Ashleigh Barty 6-1 6-4 - plays Danielle Collins next
That's us done for the day.
We'll be back tomorrow, when Serena Williams and Novak Djokovic are among the contenders bidding for a place in the semi-finals.
You can catch up on all the action from today over here and with the highlights on BBC Two tonight from 16:45.
See you later.
Image source, EPASo, the first of the four semi-finals are set.
Petra Kvitova will play Danielle Collins, and Rafael Nadal will face Stefanos Tsitsipas.
BBC Two
If you've missed any of today's action, you can watch highlights of all the best bits on BBC Two from 16:45 GMT.
Astonishing.
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Rafael Nadal, speaking on court: "I had some troubles in this event last year. To be back into the semi-finals means everything to me.I want to say thank you very very much to everybody. To be able to play here is always special."
Up next for Rafa is Roger Federer's conqueror.
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Rafael Nadal: "I said a couple of rounds ago the young guys can wait a little bit, but it looks like they don't want to wait! They are there now. It's going to be a great year in terms of sharing generations that make this sport special. that will be interesting. Let's see what happens."
Russell Fuller
BBC tennis correspondent at Melbourne Park
Big cheer for Frances Tiafoe as he leaves the court in a breakthrough Grand Slam for him.
Frances Tiafoe is stopped for a hug by John McEnroe as he makes his way off court.
He's had a fortnight to remember.
Russell Fuller
BBC tennis correspondent at Melbourne Park
That was a breeze for Rafael Nadal. He's not put a foot wrong all tournament.
Tiafoe 3-6 4-6 2-6 Nadal
Well. That's about as emphatic as emphatic gets.
Just the one hour and 47 minutes on the clock.
Tiafoe 3-6 4-6 2-6 Nadal
Rafael Nadal is into the Australian Open semi-finals!
He has yet to drop a set in this year's tournament.
Stefanos Tsitsipas awaits.
Tiafoe 3-6 4-6 2-5 Nadal*
That's a winner and a half though!
Two match points to Rafael Nadal.
Tiafoe 3-6 4-6 2-5 Nadal*
Oops.
Frances Tiafoe gets on the board in this game as Nadal whirls a forehand long for 15-30.
Tiafoe 3-6 4-6 2-5 Nadal*
Ace.
Ace.
30-0.
Tiafoe 3-6 4-6 2-5 Nadal*
Here Rafa goes.
Simon Briggs
Daily Telegraph tennis correspondent on BBC Radio 5 live sports extra
I think Tiafoe will get back to his hotel tonight and think about the lessons he can learn from this and how far he has to go.
Tiafoe 3-6 4-6 2-5 Nadal*
And Nadal only needs one!
He opens up the court and then sends a furious winner into the open space.
The Spaniard will serve for the match.
*Tiafoe 3-6 4-6 2-4 Nadal
A sliding Tiafoe drags his forehand into the net post before an approach to the net finally works, forcing Nadal's backhand to drift out.
It's 15-30 but Tiafoe swipes at a backhand. He nets, and Nadal has two break points.
*Tiafoe 3-6 4-6 2-4 Nadal
Relentless from Nadal.
A full return onto the baseline confounds Tiafoe, who nets, and Nadal cracks down an ace as he hurries along to a hold.
Image source, EPA