On Sunday, I spent much of the morning looking at a shiny red car that had been placed behind the players inside the center court in Madrid. On Monday morning I was greeted with a new view, of the white statues and marble rows of seats that surround those same players in Rome. The Caja Magica made progress this year, but there’s only one Foro Italico, and there’s no mistaking it. You can feel its chaotically slouched, sunnily cigarette-stained Old World atmosphere right through the TV screen. Like its home city, it’s eternal.

As you must have gathered from that first paragraph, play has begun in Rome. In fact, two full days have already have gone into the books while I’ve been watching and writing about Madrid. Before we fall any farther behind, here’s a look at the men's and women's draws, and what we might see in the week ahead. I’ll start with the men.

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First Quarter (ATP)

The first piece of news to report is that Novak Djokovic and Rafael Nadal have landed in the same half. They haven’t met in a semifinal since 2009, but that streak could be broken here.

Djokovic likes Rome; he’s won twice, and lost to Rafa in the final two other times. From what I remember, he has also been treated well by the fans, something he should appreciate after the whistles he heard in Madrid. He should also be sharper than he was last week, when he was still in recovery mode from his recent ankle injury. Novak starts with veteran clay dog Albert Montanes tomorrow and could get an intriguing match with Madrid finalist Stan Wawrinka after that. Nole beat Stan in the final here in 2008, and we all remember their classic in Melbourne in January. If they do play, we’ll get an early idea of how far Wawrinka may be able to progress this season. Djoko hasn't lost to Wawa in almost seven years.

Tomas Berdych is on the other side of this section. Can he recover from his last-second meltdown to Wawrinka in the Madrid semis? He lost to Nadal in the quarters here last year, and has landed in the trees this time around. Istomin, Anderson, and Cilic are the three players closest to him in the draw.

Potential second-round match to watch: Wawrinka vs. Dolgopolov

Semifinalist: Djokovic

Second Quarter

Call this the déjà vu section: Nadal and David Ferrer are scheduled to play in the quarters, as they did on Friday in Madrid. Each should have a little extra motivation for this one. If they play and Ferrer wins, he locks up the No. 4 seed at Roland Garros; if they play and Nadal wins, and goes on to win the title, he’ll steal that spot from his friend Ferru.

Ferrer’s draw looks manageable. He’ll open against either Zeballos or Verdasco, and then should get Philip Kohlschreiber. Nadal, a seven-time champion here, starts with Fognini, a home favorite who will have the crowd behind him. That could be tricky for a bit, until Fognini realizes who he’s trying to beat. Also on this side is Ernests Gulbis, who took Nadal to three sets here a few years ago, and lucky loser Lukas Rosol. We know what he did against Rafa.

Third-round match to hope for: Nadal vs. Rosol

Semifinalist: Nadal

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Third Quarter

Clay hopefuls and unreliables—Andy Murray, Juan Martin del Potro, Nicolas Almagro, and Kei Nishikori—gather here. Neither Murray nor del Potro has had a good spring in Europe thus far. The Argentine, who pulled out of Madrid with an illness, has won a total of one match since his runner-up finish in Indian Wells two months ago. The Scot, despite much talk about his new focus on dirt, hasn’t fared much better, going out in straights to Wawrinka and Berdych in Monte Carlo and Madrid, and hardly looking more comfortable on clay while he was doing it.

But each has a decent shot at the semis in Rome. Del Potro opens against qualifier Andrey Kuznetsov and could see Almagro in the third round. Murray starts with Marcel Granollers and might get Nishikori after that. Who is going to finally come through among them? I’d like to say Nishikori has a shot, but he’s 0-7 in sets against Murray for his career.

Semifinalist: Murray

Fourth Quarter

After his rusty clay kick-off in Madrid, Roger Federer will try to build some momentum in Rome, starting tomorrow night against Italy's own Potito Starace. Federer has reached the final here, and he made it to the semis last year, but he’s taken his lumps at the Foro as well, including an ugly upset at the hands of Ernests Gulbis three years ago. We’ll see what we get from him in 2013. A potential third-rounder against fellow father, and one-hander, Tommy Haas could be good.

Second-round matches to watch: Tsonga vs. Janowicz; Gasquet vs. Dimitrov

Semifinalist: Tsonga

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Semifinals: Djokovic d. Nadal; Murray d. Tsonga

Final: Djokovic d. Murray

First Quarter (WTA)

Serena Williams has won her last three tournaments; can she make it a fourth, as well as pull off the difficult Madrid-Rome double? It proved to be too much to ask, physically, in 2012, when Serena withdrew with a back injury before the semis at the Foro against Li Na. This time, seemingly in good shape after her straight set romp over Maria Sharapova on Sunday, she’ll start against Laura Robson tomorrow night. The two have never played, though Serena did watch Robson beat her sister, Venus, on Monday afternoon.

Not having to play Venus was a help for Serena, and, as if she needed any more, she also got some from No. 6 seed Angie Kerber, who withdrew with an abdominal injury. That leaves No. 11 Nadia Petrova as the next highest seed in this section. Petrova plays Carla Suarez-Navarro to start.

Surprise thus far: Melanie Oudin got her first main-draw win of 2013 on Monday, when Ekaterina Makarova retired against her down 2-4 in the third set.

Also here: Anastasia Pavlyuchenkova

Semifinalist: S. Williams

Second Quarter

Li Na and Aga Radwanska: Remember them? Neither spent much time in Madrid—Aga was rolled in round one by Laura Robson, while Li got the same treatment from another teenager, Madison Keys. Now they’re scheduled to face each other in the quarters here.

Li, who was just a few points from the title in Rome last year, would seem to have the better chance of bouncing back, though she could have a tricky opener, against either Rybarikova or her countrywoman, Jie Zheng. After that, Li might play either Jelena Jankovic or Caroline Wozniacki. Meanwhile, Radwanska could face a challenge from Italian Roberta Vinci, who beat her at the U.S. Open last year, in the third round. If Aga loses that, she might begin to wonder if blondes really do have more fun.

First-round match to watch between players who could use a win: Caroline Wozniacki vs. Bojana Jovanovski. Caro lost first-rounders in Stuttgart and Madrid, while Bojo is 0-7 since the Australian Open.

Semifinalist: Li

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Third Quarter

Maria and Serena have had the field mostly to themselves the last couple of months. Isn’t it time for Victoria Azarenka to join them again? She earned one win, as well as a code violation for racquet abuse, in her first tournament back, in Madrid. This week Vika starts against the winner of Goerges and Hlavackova, and could play a resurgent—for the moment—Ana Ivanovic after that.

On the other side, No. 8 seed Petra Kvitova will open with what's sure to be a wild ride against Sabine Lisicki—it’s not often that the Czech faces someone more erratic than she is, but Lisicki might just qualify.

Also here: Sam Stosur, Rome runner-up in 2011. The Aussie won her first match of the European clay swing on Monday.

Semifinalist: Azarenka

Fourth Quarter

Last year Maria Sharapova lost to Serena Williams in Madrid, and followed it with a title in Rome. Is a repeat performance possible? She’ll start against hard-hitting Spanish youngster Garbine Muguruza, and might see Sloane Stephens, another young player who could use a win, in the third round.

Scheduled to await Maria in the quarterfinals is Sara Errani. That would be interesting if it happens. Errani is a home favorite, she’s coming off a semifinal run in Madrid, and she tested Sharapova severely in Miami last month. The Italian will open against either Karin Knapp or Christina McHale.

Semifinalist: Errani

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Semifinals: S. Williams d. Li; Azarenka d. Errani

Final: S. Williams d. Azarenka