American tennis has long feared what might happen when the Williams sisters eventually hang up their rackets but as the Australian Open reaches the business end, it seems they have nothing to worry about.

Not only is Serena Williams still the undisputed No 1 and, despite some indifferent form, into the last eight; but sister Venus Williams is rolling back the years and in Madison Keys, they have a future star who was inspired to play tennis because of the Williams sisters.

As she has done throughout this tournament so far, top seed Serena struggled early on but came through against Garbine Muguruza, the Spaniard who beat her at the French Open last year, 2-6, 6-3, 6-2 to reach the last eight.

Tomorrow she'll face Dominika Cibulkova, last year's runner-up who has bounced back here after a shocking second half of 2014, beating two-time champion Victoria Azarenka 6-2, 3-6, 6-3.

Serena revealed that she's been battling a nasty cough but when the going got tough, she found her best form.

"She made me play a lot better," she said of Muguruza. "I had to play the best match of the tournament or else I was going to be out. I think she was just hitting winners like left and right. Every shot I hit, she basically hit a winner on. So I had to change my approach."

But if an improving Serena Williams spells danger for the rest of the field, it is the performances of her sister, Venus, and the 19-year-old Keys that have really captured the imagination at Melbourne Park.

Just five months short of her 35th birthday, Venus continues to defy the passing of time but her form is all the more remarkable as she continues to battle Sjogren's syndrome, an incurable illness which causes chronic fatigue and muscle soreness.

Dealing with that is a daily battle for the American but yesterday she outfought sixth seed Agnieszka Radwanska 6-3, 2-6, 6-1 to reach her first grand slam quarter-final since 2010.

"From the outside looking in, I guess it could look like that," she said, when asked if it was her best win for years. "But for me I'm just really focused and poised right now. I feel like I've been here before, so it's not like I'm jumping up and down for joy.

"Now is my moment and I want to keep this moment going all year and then next year too. But that will take work."

To get to the semi-final, though, she will have to beat Keys, who continued her outstanding run with a confident 6-2, 6-4 win over Madison Brengle.

Having beaten Wimbledon champion Petra Kvitova in round three, the 19-year-old, who is coached by Lindsay Davenport, avoided a let-down and with her huge serve, powerful groundstrokes and good movement, she looks every inch a champion in waiting.

"I'm just really excited," she said. "I think it's a huge opportunity for me. I haven't been in this situation before. I'm going to make the most of it.

"But at the same time no matter what, I'm not really going to be satisfied with any win. I want to be at the end of the tournament holding the trophy up. That's my goal in the long run."