MELBOURNE, Australia — For all their Grand Slam successes, Venus Williams and Roger Federer still find themselves surprised to be in the semifinals at the Australian Open.

Injuries, illness and advancing age can do that to the best of athletes, even 17-time Grand Slam champion Federer and seven-time Slam winner Williams, who has overcome an energy-sapping illness and is playing some of her best tennis since being diagnosed with Sjogren's syndrome in 2011.

“I have a lot to give, I have a lot to give to the game. I feel like I have a lot of great tennis in me,” Williams said when asked why she didn't retire when diagnosed with the illness that also causes joint pain. “It's just the excitement of having the opportunity to compete at my best level.”

Williams, 36, beat Anastasia Pavlyuchenkova 6-4, 7-6 (3) on Tuesday, becoming the oldest player to reach the semifinals at Melbourne Park in the Open era. She'll play CoCo Vandeweghe, an American who beat French Open champion Garbine Muguruza 6-4, 6-0 in Tuesday's other quarterfinal match.

It was a long time coming for Williams, who reached her 21st Grand Slam semifinal but her first at the Australian Open in 14 years.

The 35-year-old Federer, meanwhile, is back from a six-month injury layoff after left knee surgery. On Tuesday, he had a 6-1, 7-5, 6-2 win over Mischa Zverev, the player who eliminated top-seeded Andy Murray two nights earlier.

Federer's semifinal opponent will be Stan Wawrinka, who beat Jo-Wilfried Tsonga 7-6 (2), 6-4, 6-3. But Federer didn't expect to be anywhere near the semifinals.

“Winning back-to-back matches in best-of-five sets against great players, that's been for me the big question mark,” Federer said. “I felt I was always going to be dangerous on any given day. But obviously as the tournament would progress, maybe I would fade away with energy.

“I think now that I'm in the semis, feeling as good as I am, playing as good as I am, that's a huge surprise to me.”