Her 16th Grand Slam title: Williams beats Sharapova, 6-4, 6-4, in the final of the 2013 French Open:
What happened: "J'adore Paris," Williams said during her victory speech, and that wasn't a new champion trying to charm the locals; she undoubtedly meant it. Williams has an apartment in the city. She also has a French coach in Patrick Mouratoglou, and had been working on speaking the local lingo. And her connection with Paris would only have deepened after she won the Coupe Suzanne Lenglen for the second occasion, some 11 years after holding it for the first time. It was plain that Williams was driven by the anguish she had experienced in 2012, when she had lost in the opening round of a Grand Slam tournament for the first time in her career. This was her response, going all the way through the draw after beating Sharapova, the defending champion, in straight sets.
What Serena said: "I'm still a little bit upset about that loss last year. But, for me, it's all about how you recover. I think I've always said that being a champion isn't just about how much you win, but how you recover from your downs, whether those are injuries or losses."
What her opponent said: "Serena is playing extremely well - she's a competitor."
What others said: "Serena feels a bit at home here in Paris," said Mouratoglou.
The statistic of the match: Williams, 31, became the oldest woman in the modern era to win the French Open.
A memorable moment: During her speech, Williams also said: "Je suis incroyable." What she had meant to say was: "I can't believe it." Instead she had announced: "I am incredible."
Her 17th Grand Slam title: Williams beat Azarenka, 7-5, 6-7, 6-1, in the final of the 2013 US Open:
What happened: Williams at the US Open is never an off-Broadway production; she and Azarenka produced almost three hours of theatre in Queens on the cement of the Arthur Ashe Stadium. Williams had her opportunities to win this final in straight sets - she led 4-1 in the second set with a double break, and twice served for the set and the match, but Azarenka hung around and took this into a decider. Eventually - after two hours and 45 minutes - Williams defeated Azarenka for the second successive year, and was the US Open champion for the fifth time. The victory left her just one Grand Slam title short of Chris Evert and Martina Navratilova, who each won 18 majors.
What Serena said: "I had felt disappointed with my year, to be honest. I felt like, yeah, I won the French Open, but I wasn't happy with my performances at the other two Grand Slams [she was beaten in the quarterfinals of the Australian Open, and in the fourth round of Wimbledon], so I definitely feel a bit better with at least a second Grand Slam under my belt this year."
What her opponent said: "Serena is a champion and she knows how to repeat that. She knows what it takes and how to get there. I know that feeling, too, so when two people who want it so bad meet, it's like a clash. It's a tough loss, but to be in a final and to play against the best player, who deserves to win, it's incredible. I gave it my all today, and we both showed our hearts. We fought hard."
What others said: "I think Serena has a real sense of history right now, and she is defining her place in history," Chris Evert told ESPN.
The statistic of the match: It was the longest ever recorded women's final at the US Open.
A memorable moment: "I can't play in the wind," Williams said to her team at one point during the match, and it's true that the weather conditions didn't allow the two finalists to time the ball as sweetly as they would have liked.
Her 18th Grand Slam title: Williams defeated Wozniacki, 6-3, 6-3, in the final of the 2014 US Open:
What happened: Had Williams lost this final, she would doubtless have considered it to have been a wasted year at the Grand Slams. She hadn't even reached a quarterfinal at the first three majors of the season, so defeat in New York would have meant a blank for 2014. Wozniacki is a close friend, but that was hardly going to prevent Williams from playing aggressive tennis. After all, playing a friend in a Slam final is always going to be easier than playing your sister. It was a determined Williams who scored a third successive title at Flushing Meadows, and her sixth overall, which took her to the magic number of 18 majors, the same number that Chris Evert and Martina Navratilova had each won during their respective careers. But, almost immediately, she started to think about winning a 19th major.
What Serena said: "I definitely overdid it and put too much pressure on myself for 18, but at least I'll learn. Going into the next Slam, there will be no pressure. It's crazy - everyone's like, 'Well, Serena hasn't won a Grand Slam'. I could name 200 people who haven't won a Grand Slam as well. But it's fine, it's like I have to win a Grand Slam because everyone expects so much out of me. And I do, too. I definitely do, too. It's just really good to have won one this year. I was getting nervous."
What her opponent said: "Serena, you really deserved it today. You're an unbelievable friend, and you definitely owe drinks later."
What others said: "As they say in Queens, that's a whole lot of lettuce," Mary Carillo said after William was presented with $4 million, the largest cheque in the history of tennis. That figure was made up of $3 million in prize money and a bonus of $1 million for winning the preceding US Open Series.
The statistic of the match: This victory came 15 years after Williams had won her first Grand Slam title at the 1999 US Open.
A memorable moment: To welcome Williams to the club of women who had 18 Grand Slams, Evert and Navratilova presented her with an 18-carat gold Tiffany bracelet.
Her 19th Grand Slam title: Williams defeated Sharapova, 6-3, 7-6(5), in the final of the 2015 Australian Open:
What happened: Is it possible for one player to achieve a 16th consecutive victory over a rival and still create drama? The answer, as anyone who watched this final will tell you, is a resounding yes. Never before had Williams left the court mid-match to vomit. And this was a match full of high-quality exchanges, and tension up until the last point (which Williams needed to win twice). More importantly, consider what was on the line. Victory took Williams into outright second place in the list of the most successful women of modern times. Previously, she had been tied with Chris Evert and Martina Navratilova on 18 majors; this win took her to within three Grand Slams of Steffi Graf's 22. If you looked at all generations of tennis players - so including those from the sport's amateur era, too - then this put Williams level with Helen Wills Moody on 19, and five shy of Margaret Court, whose 24 Slams were amassed before and after tennis turned professional. This was the first time since 2010 that Williams had taken the Australian Open title - she became the first woman of the modern era to win the tournament six times.
What Serena said: "Growing up, I wasn't the richest. But I had a rich family in spirit and support, and standing here with 19 championships is something I never thought would happen. [As a kid] I went on the courts just a ball and a racquet and a hope, and that's all I had."
What her opponent said: "Serena is creating history. It's an honor playing against her. She's the best and as a tennis player, you want to play against the best."
What others said: "I think Serena can reach Steffi at 22," said Evert. "She's healthy and she's driven."
The statistic of the match: Four of Williams' six Australian Open titles have been won indoors after the roof of the Rod Laver Arena has been closed.
A memorable moment: Williams needed two aces to convert a championship point. The first time, Williams had already dropped her racquet in celebration. But the ball had touched the net on the way through, and so was called as a 'let. Many other players would have faltered at that moment. Williams didn't. She returned to the baseline and produced pretty much the same serve again, only this time it didn't brush the top of the net. Game over.
Mark Hodgkinson is the author of 'Game, Set and Match: Secret Weapons of the World's Top Tennis Players' (Bloomsbury, May 2015).