American women enjoy best US Open showing since 2002

    Story highlights

    • Williams, Keys, Vandeweghe & Stephens progress
    • Best performance by American women since 2002

    (CNN)Serena Williams' absence has not stopped America's women from enjoying their most successful US Open for 15 years.

    Madison Keys' victory over fourth seed Elina Svitolina Tuesday ensured four American women progressed to the quarterfinals in New York -- the best performance by the US since 2002, when five made it into the last eight.
      Williams, the most successful female player of the Open Era with 23 grand slam titles, gave birth to her first child last month but while the 35-year-old is on maternity leave her compatriots Keys, Coco Vandeweghe, Sloane Stephens and older sister Venus Williams have shone on home soil. Roger Federer is the most successful man with 19 grand-slam titles.
      Remarkably, ninth seed Venus was part of that American quintet of Lindsay Davenport, Jennifer Capriati, Monica Seles and sister Serena 15 years ago and is aiming for a first title at Flushing Meadows since 2001.
      Venus Williams is a seven-time grand slam champion.

      Venus v Kvitova

      The 37-year-old, who has shone in the majors this year -- reaching the Australian Open and Wimbledon finals -- faces two-time Wimbledon champion Petra Kvitova on Tuesday.
      Nine months after an intruder attacked her with a knife, Kvitova is three victories away from what would be her first US Open title.
      "What she's gone through is unimaginable, unreasonable," Williams told reporters of Kvitova, who underwent emergency surgery in the aftermath of the attack.
      "The world we live in is just shocking. For her, I think to be playing well is such a blessing."
      Sloane Stephens
      Unseeded Stephens -- who has risen 851 places in the rankings since August -- will be first on Arthur Ashe on Tuesday, taking on Latvia's Anastasija Sevastova, the conqueror of Maria Sharapova in the last 16.
      The 24-year-old American made her tennis comeback at Wimbledon this summer after being sidelined for 10 months with a stress fracture in her foot.
      Victory over Sevastova would see her progress to the semifinals of a major for the first time since the 2013 Australian Open.

      'It's really exciting'

      The last time four American women reached the US Open semifinals was 1981
      Vandeweghe and Keys will play their quarterfinals on Wednesday.
      Keys, the 15th seed, told reporters that the quartet's progress was proof of "how hard we've been working."
      "I'm not really surprised that anyone got this far, but I think we're all cheering for each other, excited that there's four of us in the quarters," said the 22-year-old, who will play Estonian Kaia Kanepi, 10 years her senior, in the last eight.
      "I think it's just really exciting. I'm really happy that none of us are playing each other in the quarterfinals."
      Vandeweghe, who is seeded 20th, will play in her first US Open quaterfinal and has the ominous task of toppling world No.1 Karolina Pliskova.
      Czech Pliskova predicted a tough contest against the Australian Open semifinalist.
      "I guess she just loves the crowd and the big stage, so she's going to always play well here on center court," the 25-year-old told reporters.
      "It will be tough. I played her last time in Stuttgart, I think, so it was clay, a little bit different story. Obviously she has a big serve."