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
*Edmund 6-7 (4-7) 6-3 3-4 Anderson
The South African takes a 30-15 lead with another huge serve, and then shows off his groundstroke skills with a punishing crosscourt winner from the forehand side after Edmund looked to have him on the run.
Anderson takes the game to edge back ahead in this third set.
Edmund 6-7 (4-7) 6-3 3-3 Anderson*
Image source, Getty ImagesKyle Edmund fizzes from side to side in a flash of pink and black, meeting everything Kevin Anderson has to offer and snaffling the point off the 11th seed.
Anderson's response is to send down an ace...
Edmund 6-7 (4-7) 6-3 3-3 Anderson*
Kevin Anderson towels himself down, before skipping off behind the baseline.
He looks to have the measure of Kyle Edmund's serve after engaging the Brit in a rally, but then can only find the net.
Edmund forces a forehand towards the feet of the tall South African and Anderson can't squeeze his way out of that one.
Good stuff from Edmund. He moves to 40-0, and puts it away with little fuss.
Judy's nailed this one...
*Edmund 6-7 (4-7) 6-3 2-3 Anderson
Bang, bang - Kevin Anderson breezes into a 30-0 lead, but is then met by some Kyle Edmund resistance in the form of a punchy backhand winner.
The British number two goes long on his next attempt, and Anderson closes out the game with a smart serve at the net.
Edmund 6-7 (4-7) 6-3 2-2 Anderson*
Fantastic serve from Kyle Edmund to move him into a 40-30 lead, catching the corner and leaving Kevin Anderson helpless.
Anderson gets the next one back, but a loose backhand is put away on the volley from mid-court by Edmund as the Brit holds serve.
*Edmund 6-7 (4-7) 6-3 1-2 Anderson
It's breezy in Melbourne, and threatening to rain...
Kyle Edmund is raining down points on his serve, a backhand that's too firm for Kevin Anderson on this occasion.
Anderson responds with a big backhand winner, before Edmund dances around a short return to hammer a forehand beyond the 11th seed.
Image source, ReutersLast year's beaten women's singles finalist Venus Williams - who lost to sister Serena 12 month ago - has started her 2018 campaign and, fittingly, is in action on the main Rod Laver Arena.
She leads the in-form 20-year-old Swiss Belinda Bencic 2-1 in the opening set. This could be a cracker.
Piers Newbery
BBC Sport at Melbourne Park
Schedule news - after a midnight start for Kyle Edmund, fellow Briton Johanna Konta will also kick off her Australian Open campaign at 00:00 GMT when she takes on American Madison Brengle on day two, out on Hisense Arena.
Heather Watson will play Kazakhstan's Yulia Putintseva - the "pocket battleship" as Watson described her - in the fourth match on court 13, so around 07:00 at a guess. Time for a snooze between Brits.
*Edmund 6-7 (4-7) 6-3 1-2 Anderson
That's game Kevin Anderson. He holds. It's tough, tight... and pretty tense.
Edmund 6-7 (4-7) 6-3 1-1 Anderson*
Ouchy. That thundering Kevin Anderson serve really reveberated off the strings of Kyle Edmund.
Anderson moves into a 30-15 lead, and Edmund catches the net as the giant South African makes it 40-15.
Edmund 6-7 (4-7) 6-3 1-1 Anderson*
Edmund comes storming into the net and smashes a volley beyond the reach of Anderson.
Anderson can only poke a raquet at fierce first serve and then sends the next point wide as Edmund goes 40-15 up.
The British number two toys with his opponent as he thumps a forehand one way and follows up with a backhand winner the other.
*Edmund 6-7 (4-7) 6-3 0-1 Anderson
Well, encouraging stuff from Kyle Edmund in set three, but he can't stop Kevin Anderson from holding serve.
Edmund 6-7 (4-7) 6-3 Anderson*
Kevin Anderson opens up the third set with a forehand winner, but Kyle Edmund gets himself on the board off the second.
Punchy stuff from the British number two, as he flings a powerful, curving forehand just inside the line to make it 30-30.
Mark Woodforde
12-time Grand Slam doubles champion on BBC Radio 5 live sports extra at Melbourne Park
Kyle played a very smart service game and didn't expose his second serve to Kevin Anderson.
Edmund 6-7 (4-7) 6-3 Anderson*
Lovely from Kyle Edmund, working Kevin Anderson out to the South African's right and then whipping a forehand winner into the space left behind.
He's levelled it up.
*Edmund 6-7 (4-7) 5-3 Anderson
Kyle Edmund serving for the second set then.
He moves swiftly into a 15-0 lead but can't wrap his raquet around a punchy Kevin Anderson return and pops a forehand wide.
Edmund takes the next two points. He has two set points to play with.
Image source, ReutersIt was all going so well for Sloane Stephens on Margaret Court Arena but no longer.
The US Open champion took the first set 6-2 and served for set at 5-4 in second set against China's Zhang Shuai but has just been taken to a decider, losing a tie-break 7-2.
Zhang has now broken serve in the opening game of the final set.
Stephens' results have been woeful since the US Open and her fragile confidence is facing a big test now.
*Edmund 6-7 (4-7) 5-3 Anderson
Kevin Anderson retreats to serve and volley tactics, and polishes off his service game to love.
Edmund 6-7 (4-7) 5-2 Anderson*
Kyle Edmund shrugs his shoulders as the ball trickles off his strings, there was nothing he could do about the stinger of a first serve from Kevin Anderson.
He gets the measure of the second, sends Anderson on the run and then attempts a sliced drop shot, but it drops short of the net.
That was from the school of Andy Murray, Edmund just hasn't quite graduated - yet.