|2018 World Championship|
|Venue: Crucible Theatre, Sheffield Dates: 21 April - 7 May|
|Coverage: Watch live across BBC One, BBC Two, BBC Red Button, Connected TV, the BBC Sport website and mobile app.|
Four-time champion John Higgins fought back from 7-3 and 11-9 down to complete a gripping 13-12 Crucible win over Judd Trump and reach the semi-finals.
Scotland's Higgins, who resumed the day 5-3 down, looked out of sorts and in serious trouble at 7-3 behind, but reeled off five in a row to lead 8-7.
Trump's three-frame burst and two shared frames put him 11-9 in front.
Two fine pressure 70s and a 134 put Higgins ahead and, after Trump levelled, the Scot won through.
Earlier two-time champion Mark Williams finally broke Ali Carter's stubborn resistance to earn a 13-8 win and join Kyren Wilson and Barry Hawkins in the last four.
Williams faces Hawkins in the semi-finals, while Higgins takes on Wilson.
Higgins hits back to stun Trump
The chances of Higgins reaching an eighth World Championship semi-final looked remote as Trump stretched his overnight lead to 7-3 thanks to a break of 89 and a frame stolen on the pink and black.
Higgins, 42, had been 64 points ahead in the 10th and was some way off the form which saw him crush Trump's good friend Jack Lisowski 13-1 in round two.
But the world number five showed his resilience by knocking in four more half-centuries in the next three frames to get back to within one at 7-6 and an outrageous fluked green in frame 14 tied the scores.
Higgins then knocked in his eighth break of more than 50 in the match to edge in front before Bristolian Trump responded to level matters and set up an intriguing final session.
The 30-time ranking event winner lost the opening two, but then was at his ruthless best to edge ahead and held his nerve after Trump forced a fascinating decider.
"What probably made my win it was I enjoyed it," Higgins said.
"It must be heartbreaking for him but for me to come out winning is a brilliant feeling.
"I don't know what it is but we seem to play classics all the time. He was the better player in the match and I was hanging on to his coat tails. He must hate the sight of me."
Williams on course for third world title
This year's success means the rejuvenated Williams, a two-time ranking event winner this season, has reached a first World Championship semi-final since 2011.
The 43-year-old Welshman edged a high-quality afternoon session 5-3 to take a 9-7 advantage into the evening.
Breaks of 114 and 54 put world number seven Williams in control at 6-4 up, but Carter replied with a fine 85.
Williams made it 7-5, before world number 15 Carter, 38, took a tense frame 13 on the black.
However, the 2000 and 2003 champion won two of the next three, closing the session with his third ton of an enthralling tie for a 9-7 lead over the Essex man.
He dominated session three, compiling two breaks of 113 and ended up victorious thanks to four tons and five breaks of more than 50.
Williams said: "It's going to be special and I will enjoy it more than any other semi-final I have been in.
"The tour is getting stronger, the standard is going up, I am getting older and I don't know how many more semi-finals I will get in.
"I am playing some of the best stuff I have played for years. I am playing with a lot of confidence and feel relaxed."
Wilson makes Crucible breakthrough
World number nine Wilson was in devastating attacking form throughout his 13-6 win over Northern Irishman Allen to reach the Crucible semi-finals for the first time in his career.
The 26-year-old romped into a 7-1 lead after Tuesday's second session, scoring a ton and two breaks in the 90s for an 11-5 lead.
Allen pulled one back when play resumed on Wednesday, but missed a simple blue in frame 18 and Wilson pounced on that error and another mistake in the next frame to progress.
Wilson, who was playing in his third World quarter-final in a row, has made three finals this season - including the Masters in January - where he was beaten by world number 16 Allen.
He said: "It was always a goal of mine to reach the one-table set-up and I cannot wait to get out there and experience it.
"Sometimes you have to seize on your opponent when you sense a little bit of weakness. I could feel that Mark was maybe struggling a bit towards the end of last night. Every little mistake he made, I punished him.
"I was really pleased with my performance. I played really well. My temperament was good. My long game and safety were there. And my break building was there."
Clinical Hawkins completes Ding rout
Earlier, world number six Hawkins completed a dominant 13-5 win over Ding - the favourite and highest seed left in the tournament.
Hawkins, the 2013 runner-up, scored eight half-centuries and a 113 to lead the Chinese star 11-5 overnight.
A scrappy opening frame on Wednesday went the way of the Englishman, 39, and the left-hander won his fifth frame in a row with a break of 124 to see off an out-of-sorts world number three.
Hawkins, 39, said: "I punished him every time he made a mistake and when someone is doing that against you, it is easy to miss a few.
"I managed to keep him under pressure. And there is a lot of pressure on his shoulders too. Winning 6-2 last night was huge and I am happy to get over the line. I felt like he gave up at the end."
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