Serena Williams, above, has 15 Grand Slam singles titles and Roger Federer has a men’s record 17. Both stars enter the Australian Open at 31 years of age but show little sign of slowing down; Williams has won 35 of her last 36 matches. (Paul Crock/AFP via Getty Images)

She trained in Mauritius as 2012 drew to a close, alternating morning workouts with afternoons on the beach. More recently she has been spotted shopping on the elegant boulevards of Paris, where she spends the bulk of her time, holding hands with her French coach and reported boyfriend, Patrick Mouratoglou. And the only significant tweaking to her tennis game as she has rolled to victory in 35 of her past 36 matches has been learning to relax more.

At 31, Serena Williams is reveling in newfound balance in her life. And none of it has taken the edge off the hunger and competitiveness that drives her in her 19th year on the pro circuit, particularly when a major title is at stake.

At an age when most female tennis pros have retired, Williams remains the most formidable player on the women’s tour. And she enters the season’s first major, the Australian Open, as the favorite to win it all.

“I feel like right now I’m playing some of my best tennis,” Williams said after winning a hard-court tune-up in Brisbane, Australia, earlier this month, by crushing Anastasia Pavlyuchenkova, 6-1, 6-1, in the final. “I feel like I want to do better and play better still. I’ve always felt like I could play better.”

In the men’s draw of the tournament, which gets under way Monday in Melbourne, another 31-year-old is defying age and time. After a dazzling run of dominance by Serbia’s Novak Djokovic in 2011, Swiss champion Roger Federer reasserted his relevance last season by winning his seventh Wimbledon title and, for a time, reclaiming the No. 1 ranking.

Like Williams, Federer launches into the Australian Open as a serious challenger: a four-time victor capable of denying top-seeded Djokovic his third consecutive title, and two-time runner-up Andy Murray of Scotland his first.

No doubt, the era of Williams and Federer dominating the majors is at hand. No amount of talent or defiance can stave off the inevitable next wave of youngsters who’ll hit ever harder and sacrifice even more for the titles they covet.

But the physical and mental staying power of Williams, who has won 15 majors, and Federer, who boasts a men’s-record 17, is something to behold.

For all of their respective power and shot-making, their edge against younger rivals these days is primarily mental. They are more focused and motivated than ever to add to their cache of majors before retiring. Supremely in tune with their bodies, they’ve grown savvy about preparing for the two-week grind of a major.

“It’s a great example for everybody, that even once you reach your 30s there’s still ways to improve your tennis,” says former coach Darren Cahill, now an analyst with ESPN.

Notably missing from this year’s Australian Open is former No. 1 Rafael Nadal, who hasn’t competed since his second-round loss at Wimbledon last June because of a lingering knee injury and, more recently, a stomach illness. Nadal’s punishing style of play and relentless approach to practice have long raised concerns about his career’s longevity. It’s unclear when he’ll return.

Also missing: American Andy Roddick, who retired at the conclusion of last year’s U.S. Open, and John Isner, the country’s highest ranked man (13th), who’s sidelined by a bone bruise on his right knee.

Until some brash challenger dictates otherwise, men’s tennis remains a four-way conversation among the 31-year-old Federer, 25-year-olds Djokovic and Murray and, when healthy, Nadal, 26. They divvied up the sport’s four majors last year, with Murray making the most dramatic improvement.

Under the tutelage of former champion Ivan Lendl, the combustible Scot did a far better job managing his emotions on court. His reward: a straight-sets upset of Federer at the All England club to win gold at the London Olympics, followed by a five-sets triumph over Djokovic to claim his first major, the U.S. Open, after four runner-up finishes in Grand Slam events.

On the women’s side, top-ranked Victoria Azarenka, the hard-hitting, high-pitched shrieker from Belarus, was granted no favor by tournament officials who placed her in the same half of the draw as Williams. Azarenka’s record against Williams is 1-12.

The beneficiary could be Russia’s Maria Sharapova, who’ll avoid facing either until the championship match, should she advance that far.

But if Williams stays healthy through two weeks of hard-court pounding in the Australian heat, seeding and strategy won’t matter much.

Says former champion Chris Evert, an ESPN analyst for Grand Slam events: “In the women’s game, I think the top players look at playing Serena, and they’re hoping that she just has a bad day. It’s hard to figure out what the winning strategy is against her.”