Her 11th Grand Slam title: Williams beat Venus, 7-6(3), 6-2, in 2009 Wimbledon final:
What happened: Within minutes of winning this Wimbledon final - an all-American, all-Williams production that was played on the Fourth of July - Serena changed into a T-shirt with the mildly provocative slogan: 'Are you looking at my titles?' This was her third Wimbledon success, all three of which had come from beating Venus, and also her first for six years. One family from America now had eight Wimbledon singles titles, as to Serena's three you could add Venus's five triumphs (had Venus won, she would have been the Wimbledon champion for a third consecutive summer, as well as taking the tournament for a sixth occasion). With her victory on Centre Court, Serena held three of the four Grand Slam titles simultaneously as she was already the reigning US Open and Australian Open champion.
What Williams said: "It just feels so amazing, I'm so blessed. I feel like I shouldn't be holding the trophy, like I'm holding Venus' trophy. The trophy is named for Venus, and she always wins, so it hasn't settled in yet that I've won."
What her opponent said: "Serena was just too good, she had an answer for everything."
What others said: "The Williams sisters proved their dominance at the All England Club once more," noted the Associated Press.
The statistic of the match: Going into the final, Venus hadn't dropped a set on her last 17 appearances at the All-England Club.
A memorable moment: Their father Richard wasn't there to watch - not wanting to go through the agony of seeing his daughters competing against each other for a Grand Slam title, he had returned to America to mow his lawn.
Her 12th Grand Slam title: Williams beat Henin, 6-4, 3-6, 6-2, in the 2010 Australian Open final:
What happened: Five Australian Open titles is a significant number, and so is a dozen Grand Slams, which put Williams level with Billie Jean King, and halfway to Margaret Court's all-time record of 24 majors. It was during the prize-giving ceremony, when Williams was standing on the podium holding the Daphne Akhurst Memorial Cup, that she looked over at King, her idol, and said: "I'm tied with you now, Billie. That was my goal." This was a fine performance by Henin, who had come out of retirement for a second career travelling the tennis road, but it was Williams who dominated the third set. For the first time, Williams had won the Australian Open in an even year, and had retained the title.
What Williams said: "I feel really special that I was able to tie Billie. I didn't speak to Billie about it beforehand, but afterwards we talked. We took a picture and I was very excited. What an honor. Billie Jean is a really big mentor of mine."
What her opponent said: "I'd like to congratulate Serena - she's a real champion."
What others said: "Their was a titanic struggle, lacking only a grandstand finish, which is also true of the original Titanic," noted the Melbourne Age.
The statistic of the match: Williams became the first woman in the Open era to win the Australian Open five times.
A memorable moment: When the match was over, Williams collapsed on to her back.
Her 13th Grand Slam title: Williams beat Zvonareva, 6-3, 6-2, in the 2010 Wimbledon final:
What happened: One of the very first thoughts that Williams had after winning Wimbledon again - which gave her a fourth title at the All-England Club - was that she had surged ahead of Billie Jean King on the list of serial Grand Slam champions. So she called out towards King, who was seated in the Royal Box: "Hey Billie, I got you, it's number 13 for me." With this "very special" victory, Williams was now in sixth place on that all-time leaderboard, trailing only Margaret Court's collection of 24 majors, Steffi Graf on 22, Helen Wills Moody on 19, and Chris Evert and Martina Navratilova on 18 each. Williams felt "blessed" and "happy" to be "among such great people".
What Williams said: "It sounds ridiculous but mostly I do it [train hard] because I want to look good. When I'm out running, I'm not thinking about winning Wimbledon. I'm thinking about looking good when I'm wearing my bikini. It keeps me extremely motivated."
What her opponent said: "I wasn't able to show my best today - Serena just didn't allow me to. Of course, Serena is beatable. She's a human being, she's not a machine. I mean, it's very difficult to beat her. You have to play your best."
What others said: "Having rediscovered both her focus and her fitness, Williams' rule at the top of the game is all but unchallenged," The Independent declared.
The statistic of the match: This was the ninth occasion in 11 years that one of the Williams sisters had won the Wimbledon singles title (Venus was still ahead with five). The only interruptions had been Maria Sharapova (2004) and Amélie Mauresmo (2006).
A memorable moment: Turning to her family, Williams held up 10 fingers and then another three.
Her 14th Grand Slam title: Williams beat Radwanska, 6-1, 5-7, 6-2, in the 2012 Wimbledon final:
What happened: For Williams, every title is special, but this one was "super special". This was her first major title for two years, since the 2010 Wimbledon fortnight; more significantly than that, this marked her return from the near-fatal pulmonary embolism she had suffered in early 2011. It was also her response to the misery of Paris, where, just four weeks earlier, she had lost in the opening round of the French Open. She reacted by hiring a new coach, Frenchman Patrick Mouratoglou, and by going through the draw-sheet at the All-England Club to draw level with her sister Venus on five Wimbledon titles each. Still, she didn't have everything her own way in the final, partly a result of her own mid-match nerves, and partly because of a spirited showing from Radwanska on her first appearance in a Grand Slam final.
What Williams said: "I can't even describe it. I almost didn't make it a few years ago. I was in hospital but now I'm here and it was so worth it. I'm so happy."
What her opponent said: "Serena was serving really well. That's her weapon and that's why she has won this tournament five times."
What others said: "I've seen them all, Martina Navratilova, Billie Jean King, Chris Evert was a machine, and Monica Seles, Steffi Graf, but I believe we're watching the greatest female player that's ever played this game in Serena Williams," said John McEnroe.
The statistic of the match: Williams became the first woman in her 30s to win a Grand Slam singles tournament since a 33-year-old Martina Navratilova scored the last of her nine Wimbledon titles in 1990.
A memorable moment: On receiving the Venus Rosewater Dish, Williams jumped high off the grass.
Her 15th Grand Slam title: Williams beat Azarenka, 6-2, 2-6, 7-5, in the 2012 US Open final:
What happened: This was quite the turnaround on the Arthur Ashe Stadium. Azarenka had served for the title, and yet it was Williams, who had trailed 3-5 in the third set, who came through to take the title after winning the last four games of the match. That left Azarenka weeping, and Williams celebrating winning the tournament for the fourth time. This also completed the turnaround after the despair of losing in the first round of that year's French Open; since then, she had won Wimbledon, the Olympic title at the London Games and then the US Open. It was a personal triumph for Williams, but it was also the reward for the collective effort of the American and her coach Patrick Mouratoglou. Their collaboration couldn't have had a stronger start.
What Williams said: "I honestly can't believe I've won. I was preparing my runner-up speech because she was playing so well."
What her opponent said: "It's tough, but Serena deserves to win this match because she showed what a true champion she is. I'm honored to stand with such a true champion here."
What others said: "Now Serena is really starting to really play up to her potential, which is really great to see," said Billie Jean King. "I think she's very appreciative of her good health now after what she went through and also what her sister is going through [Venus had been diagnosed with an autoimmune disorder]. And she is maturing as a person, and you start to appreciate things in a different way as you grow."
The statistic of the match: Her fourth US Open title came 13 years after her first - no woman in the Open era had previously won Grand Slam titles over such a span of time.
A memorable moment: As Williams walked around the court with her trophy, she sang along to Prince's '1999', which the stadium DJ was playing. That, incidentally, was the year that Williams had first won her home Grand Slam.
Mark Hodgkinson is the author of 'Game, Set and Match: Secret Weapons of the World's Top Tennis Players' (Bloomsbury, May 2015).