Australian Open 10th seed Caroline Wozniacki is one those players that has been world number one yet never won a Grand Slam.
But the Dane, now happy her personal and professional life after getting engaged to golf star Rory McIlroy, believes she can go all the way at Melbourne Park this year.
Wozniacki on Thursday overcame a second set meltdown in intense heat to beat unseeded American Christina McHale 6-0, 1-6, 6-2 and make the third round, where she will play the dangerous Garbine Muguruza.
Despite the mid-match wobble, she is confident of a good run at Melbourne Park.
"I think you always believe you can win, but I still have quite a few matches to go. So I'm just thinking one match at a time," she said.
The Dane ended 2010 and 2011 as world number one but she has made just one Grand Slam final so far, at the 2009 US Open.
Her title credentials will be tested by Spain's Muguruza, who is on a hot run of form after winning her first WTA tournament at the Hobart International this month.
"She's definitely on a roll, she won Hobart," said Wozniacki. "She's playing well, she's playing aggressive. Not very typical Spanish, because she goes in and attacks the ball, plays very heavy.
"It's going to be a tough match but I'm excited about it. I'm excited to have won today and be through to the third round."