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United States' Venus Williams celebrates after defeating Russia's Anastasia Pavlyuchenkova during their quarterfinal at the Australian Open tennis championships in Melbourne, Australia, Tuesday, Jan. 24, 2017.Aaron Favila/The Associated Press

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 major champion Federer and seven-time Grand Slam singles 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.

"So anytime you feel that way, you continue. It's just the excitement of having the opportunity to compete at my best level."

The 36-year-old Williams 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 next 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 due to 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 from the tournament two nights earlier.

Federer's semifinal opponent will be Stan Wawrinka, who had his major breakthrough in Australia in 2014. Wawrinka beat Jo-Wilfried Tsonga 7-6 (2), 6-4, 6-3.

Federer won the first five games in 12 minutes, setting up a straightforward win to reach his 41st Grand Slam semifinal and his 13th at Melbourne Park.

Only he didn't expect to be anywhere near the semifinals.

"Winning back-to-back matches in best-of-five sets against quality, great players, that's been for me the big question mark, if I could do that so early in my comeback," Federer said. "I felt I was always going to be dangerous on any given day in a match situation. 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."

Another tournament surprise has been the No. 35-ranked Vandeweghe. She beat top-ranked Angelique Kerber, who won the Australian and U.S. Open titles last year, in the fourth round. Vandeweghe followed it up with an upset win over Muguruza.

Vandeweghe saved the only break point she faced in the first set with an ace, and only conceded 10 points in the 28-minute second set.

"Once I got rolling in the second, it was like a freight train," she said. "You couldn't stop it."

Williams has advanced through the tournament without dropping a set, and isn't ready to stop in the semifinals in the latest installment of her career revival.

"It's wonderful to start the year out with this appearance," said Williams, who hadn't reached the semifinals in Australia since 2003, the year she lost the final to sister Serena. "I want to go further."

Williams didn't reach the quarterfinals at any of the Grand Slams from 2011 until the 2015 Australian Open. She lost in the first round in Melbourne last year.

With her run to the Wimbledon semifinals last year, Williams became the oldest woman since Martina Navratilova (at 37 years, 258 days) in 1994 to advance so far at a major.

On Wednesday, the men's semifinalists from the other side of the draw will be determined when 14-time major champion Rafael Nadal plays Milos Raonic and David Goffin takes on Grigor Dimitrov.

With Murray and second-round loser Novak Djokovic gone, the "throwback" enthusiasts are hoping for a Federer-Nadal final, just for old time's sake.

And maybe on the women's side as well.

Serena Williams, aiming for a record 23rd Grand Slam title, plays Johanna Konta and Karolina Pliskova meets Mirjana Lucic-Baroni in the remaining women's quarterfinals on Wednesday.

So there's also the possibility of another all-Williams final, a flashback to 2003 in Melbourne.

But Venus isn't thinking about any opponent in particular, just the end result.

"Should I look across the net and believe the person across the net deserves it more? This mentality is not how champions are made," Venus Williams said. "I'd like to be a champion, in particular this year. The mentality I walk on court with is: 'I deserve this."'

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