"I have had three very nice experiences and seven terrible experiences", said Thiem, who has made the last-eight at a Slam other than Roland Garros for the first time.
The fourth set was a wild 81-minute ride that began with Thiem facing break points, saw the Austrian threaten a double break before being pegged back and then a tired Nadal miss a chance to win the match. "I like this feeling, but at the same time you feel exhausted after that", Nadal said. It was a question of a little bit of luck at the end.
Thiem also remains the only member of the top 10 that Nadal has never tackled on a hard court.
After Nadal roared back to take a 2-1 lead, the fourth set went to a tiebreak.
Nadal was on 55 winners and 49 unforced errors, winning six points less than his rival thanks to that bad first set but doing what he had to do in the end despite the fact he wasted five break points in the deciding set while Thiem had none.
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"If we skip the first set, it was a really open match from beginning to the end". Happy, of course, to be in semi-finals again, it means a lot to me.
"On clay, I think it´s one of the biggest challenges in sports to beat this guy or to compete with this guy".
Next up for Nadal will be Juan Martin del Potro, who advanced to the semis via a four-set win over American John Isner. It's cruel sometimes tennis, because I think this match didn't really deserve a loser. He saved 12 break points, including three while serving at 5-5, 0-40 in the fifth set.
The popular third seed will now attempt to take a step he has not managed since winning his only grand slam title here nine years ago and reach another final. Thiem collected 24 of the opening set's 31 points, thanks in large part to a 13-3 edge in winners.
Both players suffered in the humid conditions under the floodlights at Arthur Ashe Stadium, but Del Potro fed off the energy of the crowd, including a group of his friends who have traveled from his hometown Tandil to cheer him on. "It's good to have now two days (without a match) that probably give me the chance to be 100 percent in the semi-finals".
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Bayern should progress comfortably with Benfica and Ajax likely to battle for second place and AEK as unsafe outsiders. None of the top seeds can play each other, so Real will not be drawn in the same group as Ronaldo's new club Juventus.
When it ended, on an overhead by Thiem that sailed long, Nadal walked around the net to hug his opponent and whisper words of encouragement.
What was most impressive in a match that featured brilliant shot-making and powerful, line-clipping groundstrokes over the course of almost five hours was that Thiem looked to be the fresher player compared to the 17-time Grand Slam champion who is known for his fight on the court.
"We fought the whole match and I survived with my serve which was key".
It's Theim's best ever performance at a US Open, but commentator John McEnroe says the Austrian will need to dig deep to come back from this defeat.
He then rallied past Taylor Fritz 3-6 6-3 7-6 6-4 before beating 2017 finalist Kevin Anderson in straight sets 7-5 6-2 7-6.
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Tottenham were tenants of Wembley last season and had hoped to return to White Hart Lane, and their new stadium, this season. Arsenal , who lost to City in last season's final, face Brentford while Tottenham will host Watford .
But while Isner was playing before what could count as a home crowd, del Potro got all manner of support throughout, from the blue-and-white flags or soccer jerseys dotting the stands to the repeated singsong chants of his nickname, "Delpo", punctuated by clapping.