- Murray beats Thiem 3-6 6-4 6-1
- Scot will face Berdych in last four
- Williams beats Lisicki 7-6 (7-4) 1-6 6-3
- 700th win of Williams's career
Andy Murray will face Tomas Berdych in the Miami Open semi-finals after beating Austria's Dominic Thiem.
The 27-year-old Scot lost the opening set to world number 36 Thiem, but rallied to secure a 3-6 6-4 6-1 win.
Murray will face Czech Berdych for the first time since winning January's tense Australian Open semi-final.
Serena Williams earned the 700th victory of her career as she booked her place in the semi-finals with victory over Germany's Sabine Lisicki.
Murray recovers from slow start
Third seed Murray, who reached the quarter-finals with a 500th career victory, over South Africa's Kevin Anderson, made a sluggish start in his first meeting with 21-year-old Thiem.
In the second set, Murray capitalised on a couple of unforced errors after Thiem battled back from 3-0 down to level at 4-4, and the Briton dropped only one game in the final set.
He told Sky Sports: "I was getting myself into break-point positions and it is a fine line between going for winners and trying to finish the point and making your opponent play.
"Being a good match player is understanding when to go for your shots and when to back off a little bit."
Eighth seed Berdych beat Argentine Juan Monaco 6-3 6-4 in his quarter-final.
Murray and Berdych's Australian Open semi-final was punctuated by an exchange of words in the first set, which Murray lost before winning in four.
Murray, whose ex-coach Dani Vallverdu works with Berdych, also defended his fiancee Kim Sears after the match for an apparent outburst aimed at Berdych's team.
Williams claims 700th career win
World number one and top seed Williams overcame a dreadful second set to beat 27th seed Lisicki 7-6 (7-4) 1-6 6-3 and reach the last four.
The American became only the eighth player to win 700 WTA matches, although she is still well behind Martina Navratilova with 1,442.
She faces Romania's Simona Halep for a place in the final after the third seed beat American Sloane Stephens 6-1 7-5.
Williams, 33, was set to play Halep in the semi-finals at Indian Wells earlier this month but pulled out with a knee injury, before Halep beat Jelena Jankovic in the final.
Victory for Williams, who is seeking an eighth Miami title, extended her winning run to 19 matches this season.
Lisicki, 25, failed to convert a set point in the first set before losing the tie-break, but recovered from being broken in the first game of the second set to win the next six games.
However, Williams recovered to seal victory in just over two hours.