The current world number eight was unable to defend his 2021 title in January, having been caught up in a scandal over COVID-19 entry requirements.
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The world number one had hoped to equal Roger Federer’s record of 20 grand slam singles titles but that will have to wait after fifth seed Thiem powered his way to a 7-6 (3) 7-6 (4) 4-6 7-6 (6) victory to set up a clash with Alexander Zverev.
She will bring her impressive career to a close at the Australian Open, where she won her first Grand Slam title in 2018.
The top seed was in visible pain on court and Cilic of Croatia will now face British number two Kyle Edmund in the semi-finals following his 3-6 6-3 6-7 (5-7) 6-2 2-0 victory
The 12-time Grand Slam champion stepped off the ATP Tour following Wimbledon, where he retired during his quarterfinal against Tomas Berdych because of an elbow injury.
The 35-year-old American served up 10 aces and thumped 25 winners over 75 minutes on Rod Laver Arena to join sister Venus in the last four, where she will play 34-year-old Croatian Mirjana Lucic-Baroni
The world number 12 will play 2014 champion, Stan Wawrinka, in the quarter-finals after beating Britain’s Dan Evans on Sunday