Williams has won the title at SW19 seven times and made the final in back-to-back years prior to her pregnancy-related absence in 2017.
Twenty years after making her Wimbledon debut, Williams looks as good as ever and she moves into the quarter-finals without dropping a set in her first four matches.
Serena Williams' Wimbledon tournament rolls on, as the women's quarterfinals will be without a top-10 player for the first time in the Open era. Despite the two-year gap since their previous meeting, Williams professed to having watched 52nd-ranked Giorgi play "a lot".
When Williams was asked her expectations after winning her first match at Wimbledon in two years, she said, "Not only do I expect to win, I expect to win emphatically".
Williams will next face No. 13 seed Julia Goerges on Thursday in the semifinals.
Williams is playing only her fourth tournament since returning to the Tour after giving birth to daughter Alexis Olympia nine months ago and arrived with a ranking of 181, although she was bumped up to the 25th seed.
She has won 19 straight matches at the All England Club and will appear in her 11th semifinal.More news: Sanctions to remain until North Korea 'final' denuclearisation: Mike Pompeo
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It's okay, Serena, just keep your eyes on the prize at Wimbledon!
It also took her until her 42nd Grand Slam appearance to finally get through to the last four at a major. "For me, there's so much further I want to go to get back where I was, and hopefully go beyond that".
Once Williams had figured out how to break the Giorgi serve, though, in the fourth game of the second set, the momentum changed.
In the last men's quarterfinal, which was suspended because of darkness after the third set Monday night, 2009 US Open champion Juan Martin del Potro defeated Gilles Simon of France, 7-6 (7-1), 7-6 (7-5), 5-7, 7-6 (7-5).
"But this is only my fourth tournament back so I don't feel any pressure and have to win this", she added.
The tall Czech answered an early break with one of her own but 20th seed Bertens secured a second break with a superb touch volley to move 5-3 ahead and then held easily.
Still, Williams said she's not getting too excited as she's still adjusting to tennis after returning from maternity leave.