Their journeys have entailed far more than five consecutive match-wins at the All England Club. Consider the challenges faced by our four Wimbledon semifinalists:

Barbora Krejcikova, struggling with a back injury, won three matches in a span of five months coming into this fortnight.

Donna Vekic considered retiring more than a few times after a series of devastating injuries in 2021 and 2022 -- and now she’s through to the first Grand Slam singles semifinal of her career.

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Jasmine Paolini, who won a single match (in qualifying) in six previous appearances at Wimbledon, finds herself one win away from her second consecutive major final. Her 14 wins in Grand Slams this year are more than any other woman.

After withdrawing from Indian Wells and Rome, where she was the defending champion, and retiring from her second match three weeks ago in Berlin, Elena Rybakina seeks to win her second Wimbledon title in three years.

Perseverance, intestinal fortitude, determination, tenacity -- in a word, belief -- got them to Thursday’s Wimbledon semifinals. Here’s a closer look:

No.4 Elena Rybakina vs. No.31 Barbora Krejcikova

The case for Rybakina: The math is pretty simple. The 25-year-old representing Kazakhstan has played 21 career matches at Wimbledon -- and won 19 of them.

That’s better than 90 percent, the second-best performance of the Open Era among players with at least 20 matches following Stefanie Graf.

The most recent victory was a 6-3, 6-2 blowout of Elina Svitolina, looking for her third semifinal in a six-year span. It was over in 61 minutes and the final point -- an ace outside at 113 miles per hour -- was the emphatic exclamation point. It was Rybakina’s seventh ace and her 28th winner.

“Elena, she’s a big striker,” Svitolina said later. “She’s not letting you so much into the match. The game that she broke me in the first set, she hit like four great returns, even though I served first serve. Yeah, was tough for me to do anything on those balls. 

“Then she has a big serve, so sometimes it goes like this -- especially on grass.”

Rybakina has stroked 31 aces through five matches, more than any of the semifinalists. And it’s not just her power, it’s the placement, too. On the increasingly crusty Centre Court, her serve is a huge advantage.

This is Rybakina’s seventh semifinal of the year, and she won five of her previous six. She also won her two previous major semifinals in straight sets. Rybakina will be supremely motivated to win a second Wimbledon title.

“Back then of course I was not expecting to be that far in the draw,” she said. “Now with all the experience and with the time which passed of course, I come and I want to be in this stage of the tournament. Yeah, just much more experienced player for sure now and know what to do. 

“But there is nerves every time you go on the court. This is still the same, but I think I’m managing much better than before.”

The case for Krejcikova: She comes in as a significant underdog, but here are two reasons not to discount Krejcikova’s chances:

1)    After defeating Jelena Ostapenko 6-4, 7-6(4), Krejcikova is 5-2 in Grand Slam draws against former major champions. Rybakina, we remind you, is a major champ.

2)    The two have played twice before and Krejcikova won both of them -- three years ago in Melbourne and in the 2022 Ostrava semifinals. Krejcikova came back twice after losing the first set.

Krejcikova’s already two wins better than her best previous singles effort here, the fourth round in 2021. Krejcikova went 3-2 the past two years and is thrilled with her performance, which includes a trip to the quarterfinals (at least) in doubles with Laura Siegemund.

“I always wanted to play here,” Krejcikova said. “I always wanted to be part of the singles competition. I played many, many times in Roehampton, tried to qualify. It wasn’t really working. Then in 2021 I finally did my debut here. For me being here at the Wimbledon, being part of the competition and being part of the traditions, strawberries and all white, all this, I mean, I really like it.

“It’s something that I like that’s little bit also part of my personality. I like all this history stuff and the tradition. It’s an honor and a dream come true to be here and play at the Wimbledon.”

As mentioned above, it’s been a streaky year for Krejcikova, but she has a knack for rising to the major occasions. The only other time she reached a Grand Slam singles semifinal she won the tournament -- the 2021 French Open.

She’s beaten two Top 15 players (Ostapenko and Danielle Collins) in consecutive major matches for the first time and, again, Rybakina is ranked No.4 among Hologic WTA Tour players.

No.7 Jasmine Paolini vs. Donna Vekic

The case for Paolini: It’s been a transformative year for the 28-year-old Italian, who is generously listed at 5-foot-3. Her quarterfinal match against Emma Navarro neatly frames her breathtaking breakthrough.

Paolini had lost all three matches to the American (in a span of nine months) but came through with a definitive 6-2, 6-1 victory. After being broken in the third game, Paolini won 11 of the last 12 games. Leave it to Navarro to explain what happened.

“She was a totally different player today than when I played her in the past,” Navarro said. “I felt like in our previous meetings I was the aggressor, I was the one controlling points. I felt just the opposite of that today. I felt like she was just on top of me from the very first point.”

Paolini began the year ranked No.30 among Hologic WTA Tour players and will be at least No.5 come next Monday. That’s what happens when you lace together a WTA 1000 title on hard courts (Dubai), a Grand Slam final on clay (Roland Garros) and now a major semifinal on grass.

The last one is the hardest to process. Her coach, Renzo Furlan, has been telling her she has the game to succeed on grass, but Paolini wasn’t so sure.

“I wasn’t believing too much,” Paolini told reporters. “I think also the last two years I played against [two-time Wimbledon champion Petra] Kvitova first round, so it was tough to believe it. I felt great also in Eastbourne. I was hitting well the ball on this surface, moving well. I was repeating to myself, `OK, it’s nice to play on grass. You can play well.’”

Paolini leads Vekic 2-1 in their head-to-head, and Paolini won their most recent match, last summer in Montreal.

If she plays like she did against Navarro, Paolini could become the first woman to play in the championship match at both Roland Garros and Wimbledon in the same year since Serena Williams in 2016.

The case for Vekic: A few minutes after Vekic came back to beat qualifier Lulu Sun 5-7, 6-4, 6-1 in the quarterfinals, she was asked what was going through her mind.

“I don’t even know, honestly,” the 28-year-old from Croatia said, wiping away tears. “She really pushed me to my limit. I felt like I was dying out there the first two sets.”

And then she won six of the last seven games -- losing only two points on her serve -- to complete a career first. In her 43rd major, she reached the final four for the first time. Only four women in the Open Era took longer, hence those tears.

After losing in the third round at Roland Garros, Vekic attacked the grass season with a vengeance. Wimbledon is her fourth event in just over one month and she’s won 10 of 13 matches. 

Her thoughts of retirement, particularly after a difficult knee surgery, are well known but after beating Sun, Vekic revealed she had been wavering as recently as late May.

“It was the Thursday before Roland Garros this year that we had scheduled practice,” she said. “I arrived to the club. I told [coach Nikola Horvat], `Listen, I want to pull out of French Open. I want to go home.’ I didn’t have any energy, any motivation to keep practicing, keep pushing because I felt like the last couple months I’ve given everything for tennis, and I wasn't getting the results that I expected.”

Vekic played on and lost in the third round to qualifier Olga Danilovic -- in a third-set tiebreak.

“That loss in Paris was so, so painful,” Vekic said. “But it motivated me again to keep working, to keep pushing. I think not just in tennis, in life things can turn pretty fast.”