The Briton showed huge resolve on Centre Court to fight back for a 6-7 (2-7) 7-6 (7-5) 6-4 victory against Halep - who would have become world number one with a win - and will be the first British female since Virginia Wade in 1978 to reach the last four.
To get to what would be her ninth final at the All England Club, the 10th-seeded Williams will need to win Thursday against No. 6 Johanna Konta, the first British woman in the Wimbledon semifinals since Virginia Wade was the runner-up in 1978.
Johanna Konta marched into the Wimbledon quarter-finals yesterday afternoon, the first British woman to do so since 1984, and promised that she still has more room for improvement in her tenacious powerful game. It comes exactly a week after ticketholders saw two successive matches on the same court finish in the second set as players retired hurt. But she kept going, and with her recent successes, a championship this week would return the American to the top five in the rankings for the first time in six years. "I was fighting. That's the key for getting your confidence and playing better with every match", she said.
After the contest, a clearly emotional Konta admitted just how tricky it has been to get past her French opponent. Wade won the title a year earlier, however.
"It's humbling that I have such champions thinking so highly of me", she added.
In the opening seven days of play at this year's competition, 14 matches on Centre Court have been from the men's singles draw, with just eight coming from the women's. "I text her the game plan the night before and she reads it" her coach Wim Fissette told Press Association Sport.
However, Ostapenko doesn't handle changes of pace that well and I'm sure Venus will attack her second serve.
"It showed in the end that both players were so good but she had a tougher mind and she was more aggressive and she deserved to win".
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A feisty Halep didn't back down when questioned about the situation following her victory over Victoria Azarenka. However, the 20-year-old Latvian won the girls' title at Wimbledon in 2014.
Here, we list a few things you should know about Konta..
And if she beats Konta to earn a second successive quarter-final in a major, following her run to the same stage at the French Open, then Garcia's big career decision will look like spectacularly smart judgement.
"It was a tremendous match, played at a very high level".
Win she did, but not in the manner she or most of those in the audience would have liked.
And while I'm talking about Kei, I think I was a little unfair when I wrote about him here last week.
She now faces Venus Williams in the semi-finals.