Paul Forsyth: The Williams sisters have their critics but remain the most likely to light up SW19

• The Williams sisters: Serena, left, and Venus

Her father, Richard, made no such effort. Before, during and after his daughter's 6-3, 7-6 victory, he held up a series of whiteboard messages for the benefit of his wife in Florida. "Miss you" was one of them. "I need a Coke," was another. At the end, he danced on the roof of the CBS commentary box, famously brandishing a sign that read: "It's Venus's party and no one was invited."

Those are the abiding memories of that seminal summer's day a decade back when Venus became the first black Wimbledon champion in a quarter of a century and the first African American to win the women's title since Althea Gibson in 1958. Serena had already achieved her breakthrough win, at the previous year's US Open, which meant that the Williams girls could now claim to be the first sisters each to win a grand slam singles title.

As we know now, that was only the beginning. The ten years since then have been a tale of domination, especially at Wimbledon, where Venus has won five singles titles and Serena three. Venus has appeared in eight of the last ten finals, earning herself a reputation as one of the game's greatest grass-court players. In four of those finals, including the last two, she has played against her sister.

Nor has their stranglehold been exerted only at Wimbledon. Serena, 28, has won 12 grand slam titles, including five Australian Opens. Venus, 30, has won seven, two of them US Opens. Together they have won a dozen doubles titles in the grand slam events, and are currently holders of all four.

Every now and then, somebody will argue that their command of the sport is unhealthy; that their unprecedented combination of power and poise has squeezed some of the life from women's tennis, ensuring that a circuit already lacking depth has become way too predictable for its own good.

Don't you believe it. TV ratings decline in their absence. Before this year's French Open final had even been played, some were speculating that the match between Francesca Schiavone and Sam Stosur would be the worst grand slam final ever. Those pining for a change of scenery ought to be careful what they wish for.

Tennis has come to depend and thrive on the Williams sisters, a bit like golf has on Tiger Woods. Just as he has introduced another white middle-class sport to the hitherto disenfranchised, so too can the products of a Los Angeles ghetto claim to have inspired ethnic minorities. A growing number of African Americans are playing tennis at grassroots level, if not yet in the professional game. Billie Jean King, winner of 12 grand slam singles titles, said in Time magazine that Serena was "one of those rare champions who have transcended sport and impacted society".

Steffi Graf won 22 grand slam titles, seven at Wimbledon. Martina Navratilova won 18, nine of them in London. If the Williams sisters' combined might seems to have had a suffocating effect on women's tennis, consider this: the eight grand slam singles finals they have contested is six fewer than those played between Navratilova and Chris Evert, whose rivalry is fondly remembered.

Evert and Navratilova weren't sisters, though. And they weren't black. Neither were they inclined to disregard the game's conventions. Richard Williams made a point of instilling in his daughters the kind of arrogance and attitude that he thought they would need to survive. For him, they would require more than talent to emerge from the 'hoods of LA, and make it on to the lawns of SW19.

Ever since he said after that first Wimbledon win that Venus and Serena wouldn't "walk the line", that they wouldn't do what America wanted, they have confronted the establishment. They have developed a tetchy relationship with the media and, by extension, the public. At this year's French Open, Venus played in lacy lingerie and a pair of see-through undies. Serena, meanwhile, is serving a two-year probationary period after her foul-mouthed threat to a line judge in last season's US Open. "I swear to God, I'll f***ing take the ball and shove it down your f***ing throat, you hear that?" said the Jehovah's Witness, who will face a lengthy ban from grand slam competition should she re-offend.

Not that she sounds in the least repentant. Serena has described her 100,000 fine as a joke, ridiculed the concept of probation and suggested that, if the feedback she has been getting is any guide, the game should be grateful for her antics. New fans are turning to the sport, and it's all because of her. "They say that after I did that, they now watch tennis, and I'm like, 'Cool'."

The Williamses divide opinion. They attract newcomers and alienate traditionalists. They have distanced themselves even from their admirers, especially after the gangland killing of their sister, Yetunde, seven years ago. Their family is that party to which no one else is invited. By setting themselves apart, they have not enjoyed the popularity of their black predecessors, Arthur Ashe and Zina Garrison.

None of which will prevent the Wimbledon crowds extending a warm welcome this week. Lip service is being paid to the potential challenge of Justine Henin and Kim Clijsters, who have both emerged from retirement, but if the Williams sisters play to their potential, another title is theirs for the taking. Although Venus hasn't gone beyond a quarter-final in this year's grand slam events, grass brings out the best in her. Her younger sister has had a poor clay-court season, but it hasn't stopped her in the past.

Serena, after all, is the defending champion, a player who won this year's Australian Open with a dodgy knee that sidelined her for the next three months. For all their shortcomings on and off the court, she and her sister are still the favourites, still ranked one and two in the world, still seeded one and two for the tournament. The domination that has lasted a decade shows no sign of letting up.

THE OTHER WOMEN TO WATCH AT WIMBLEDON

JUSTINE HENIN

Henin came out of retirement after being inspired by seeing Roger Federer complete a career grand slam by winning last year's French Open. The Belgian herself has triumphed at the Australian, French and US Opens, so Wimbledon is the only major missing from her collection, and she would dearly love to put that right after losing in two previous Centre Court finals – to Venus Williams in 2001 and to Amlie Mauresmo in 2006.

KIM CLIJSTERS

Clijsters' own comeback preceded Henin's by just a few months, and almost immediately she won the US Open last September. She has displayed mixed form since then, and a foot injury ruled her out of the French Open. However the 27-year-old should be well prepared for her latest tilt at Wimbledon, where she will be seeking to reach her first SW19 final.

SAM STOSUR

She lost to Italy's Francesca Schiavone in the French Open final at Roland Garros ealrier this month, but of the pair it seems more likely that Stosur will be a threat at Wimbledon. The Australian, pictured left, has never been beyond the third round but having enjoyed the best year of her career to date there is every chance of improving that record. Her powerful game should suit the grass.

AGNIESZKA RADWANSKA

The 21-year-old from Krakow has never failed to make an impact at Wimbledon. Junior champion in 2005, 12 months later she became the first Polish player to reach the fourth round and, after making the quarter-finals in each of the last two years, is fancied to go even further this time.

CAROLINE WOZNIACKI

This Monte Carlo-based Danish No.1 is just 19 and the 2006 junior Wimbledon champion. She reached the US Open final last year and was a quarter-finalist at Roland Garros earlier this month so a grand slam title beckons some time in the future, and maybe Wimbledon will provide that title.

LI NA

Leading the revolution in Chinese tennis, the 28-year-old was the first woman from her country to reach the world's top 20 and at Wimbledon four years ago became China's first grand-slam quarter-finalist. Also a semi-finalist at this year's Australia Open.

MARIA SHARAPOVA

The Russian pin-up, pictured left, has endured miserable luck with injury since bursting on to the Wimbledon scene in 2004 but the former champion is still only 23 and is a serious dark horse.

MELANIE OUDIN

The 18-year-old American was the WTA tour newcomer of 2009 and has maintained that promise so far this year by helping her country to Fed Cup wins over France and Russia.