Serena Williams won a thrilling encounter against fellow American Alison Riske to reach the Wimbledon semi-finals on Tuesday and take a step closer to a record-equalling 24th grand slam title. In a battling performance from start to finish, Williams mounted a fightback to win the first set, lost a tight second, and edged a topsy-turvy third to clinch a 6-4, 4-6, 6-3 victory on Centre Court. "It was really satisfying," said Williams, whose clay court season was affected by a knee injury. "I wouldn't have won that match a couple of weeks ago. "I'm glad that I was able to come through. She beat so many great players. She was really so close to taking the win today." Williams, who moved into second place overall behind Martina Navratilova's record of 120 Wimbledon match wins, was constantly cajoling herself and letting out roars during the match as her sometimes leaden-footed performance threatened to undo her. "I was really pumped, it was for a place in the semis at Wimbledon - that doesn't happen every day and it's a long, arduous road," said Williams. "I just had to just button up and play hard. "She was playing her heart out and she had nothing to lose and I realised neither did I." Seven-time Wimbledon champion Williams will face Barbora Strycova in Thursday's semi-final after the unseeded Czech produced a fine performance to defeat Britain's remaining hope Johanna Konta 7-6, 6-1. Strycova, the only unseeded player in the last four, has achieved her best grand slam performance with her previous best reaching the last eight, also at Wimbledon in 2014. "It sounds crazy, it's happening but I can't really believe it," said Strycova. "I am extremely happy and my voice is even shaking still right now. "I felt like I was playing well but she was striking the ball very quick and very hard. I got into the match and then I started to feel better and then I turned it around and the confidence was building." Former world No 1 Simona Halep recovered from a slow start to beat Zhang Shuai 7-6, 6-1 and reach her second Wimbledon semi-final. Much like her fourth round match against 15-year-old Coco Gauff on Monday, Halep initially struggled and looked in real danger when 4-1 down and facing more break points in the opening set. However, the Romanian dug in to see off the threat then played her usual percentage tennis as Zhang lost her way. "I fought hard in the first set, even if I knew I was 4-1 and she was hitting hard, I knew she would hit with a lot of power. I knew I would have to play aggressively and I did it great," 2018 French Open champion Halep said. "I have energy, I feel fresh and confident and I am perhaps playing my best tennis on grass." Seventh seed Halep will now face eighth seed Elina Svitolina, who defeated Czech Republic's Karolina Muchova 7-5, 6-4. It was 28th-time lucky for Svitolina as she finally managed to get a grip on her nerves to become the first Ukrainian woman to reach a grand slam semi-final. "It feels amazing. It is the first semi-final for me, and I actually didn’t expect it to happen here. It is exciting and I am looking forward to it already," Svitolina, 24, said. For long periods during her quarter-final match, it felt that her challenge might again fall flat. She trailed 1-4 in the first set and was broken when she went to serve for the match at 5-2 up in the second set. "I had to fight for every point, take my chances, and just try to get the extra ball over the net," she said.