Clinton and Obama do not seem particularly close personally, though in addition to cabinet and National Security Council meetings, they also meet once a week whenever she is in Washington, joined usually by Biden and Donilon. “It’s a relationship that has evolved, as you would expect, and it’s one where — and I don’t say this lightly — the president has total confidence and trust in Secretary Clinton, in her advice, in her policy views and in her representation of the United States,” Donilon told me. “It’s a total trust, and that, by the by, is also historically not always the case.” Despite their differences in upbringing, age and temperament, they share, in his words, the “common experience” of running for president, living in the White House and raising children there, “of being famous people.” When it comes to policy, both she and Obama are guided by pragmatism, a nonideological, case-by-case approach. It’s one reason that no one can really define an Obama or Clinton doctrine and why, at times, the administration has frustrated those who would have had it act more forcefully when street protests auguring the Arab Spring swept Iran in 2009 or now, as Syria savagely represses its opposition.

Clinton was the first elected official to become secretary of state since Edmund S. Muskie served a turbulent eight months at the end of the Carter administration, when Iran held Americans hostage and the Soviet Union occupied Afghanistan. Whatever she might have lacked in scholarship or experience in foreign affairs, she has made up for with a politician’s touch, inside the State Department and around the world. She has an acute attention to detail, remembering names and personal details. In a meeting, she once recalled, unprompted, an obscure article about diplomacy in tough places written by a young foreign-service officer who twice served in Iraq, Aaron D. Snipe. Two people who work in the building told me of instances in which she called to express condolences when relatives died. These gestures and her strong advocacy for the budget at the State Department have re-energized the American Foreign Service, which felt beleaguered under President George W. Bush. Clinton makes a point of visiting American embassies and consulates — 109 so far — wherever she travels to thank the diplomats and their families, as well as the local staff who make up most of the work force abroad. She became the first secretary to hold special Christmas parties at the State Department for the families of diplomats with hardship posts in Iraq, Afghanistan and Pakistan.

On matters of policy, her political experience and her travels as first lady — having tea, as it were — have served her in ways few anticipated. When she traveled to Uzbekistan in October, Clinton reminded the country’s authoritarian leader, Islam Karimov, of her previous visit in 1997. “That was such a great trip,” she bantered with Karimov, who has the demeanor of the Soviet apparatchik he once was. The next day she visited a women’s health clinic where she had been 14 years earlier. The median outside was newly sodded with grass. On a placard inside was a picture of a younger Clinton. “I’m really impressed how far you’ve come,” she said after surveying the clinic’s medical equipment. Uzbekistan’s human rights record is abysmal, and Clinton raised it in her meetings, but she won Karimov’s support for expanding the flow of supplies for the military operation in Afghanistan through what’s called the Northern Distribution Network, which became vital when Pakistan closed its borders to NATO matériel.

“The art of diplomacy is to get other people to want what you want,” Madeleine Albright told me. She and others say that Clinton’s skill as a politician turned secretary is her appreciation that a foreign leader, even an autocrat like Karimov, has his own constituencies to satisfy, his own political deals to make. “I think that she is brilliant at connecting with people on a political level,” Albright said. “No question, she knows how to do what I think is essential: putting herself in other people’s shoes.”

More recently, at the NATO meeting in Chicago in May, she found herself spending most of a tense meeting with Pakistan’s president, Asif Ali Zardari, discussing, among other things, Pakistan’s byzantine parliamentary politics. Relations with Pakistan have been one of the administration’s failures, in large part a result of its greatest success: the killing of Osama bin Laden in a raid that surprised the Pakistanis and, as even American officials acknowledge, violated their sovereignty. Clinton has labored to get the relationship back on track — twice visiting Pakistan last year — only for new crises to erupt, first an American airstrike in November that killed 24 Pakistani troops at a border outpost and more recently the sentencing of a Pakistani doctor who helped the Central Intelligence Agency in the hunt for Bin Laden.

In a conference room at the convention center near downtown Chicago, Clinton pressed Zardari to reopen the supply lines to Afghanistan and act more aggressively against Islamic insurgents who use the country as a base to kill Americans. When Zardari complained that his hands were tied, she rebuffed him. According to a senior official who attended the meeting, Clinton said: “You can’t hide behind: ‘Oh, it’s too difficult. The politics are too difficult.’ ” She offered ways for him to overcome the most contentious issue for Pakistani politicians, but still Zardari demurred. American drone strikes that were briefly suspended leading up to the meeting then resumed in earnest, even before Zardari returned home.

At times, Clinton’s empathy — and her relationships developed over more than two decades of international prominence — have come at a cost. As first lady and after, Clinton developed a friendship with Suzanne Mubarak, the wife of Egypt’s former leader, Hosni Mubarak. When protests against his autocratic rule erupted in January 2011, Clinton’s initial response was to express support for Mubarak’s government. It was a misstep that took months to overcome and even now resonates among Egyptians who believe the United States supported Mubarak far too long and for the most cynical reasons. “Our assessment is that the Egyptian government is stable and is looking for ways to respond to the legitimate needs and interests of the Egyptian people,” she said at the time. Mubarak had long been an ally of the United States, and Mrs. Mubarak was a like-minded champion of women’s issues, but as Clinton has said on several occasions since the Arab Spring, those who fail to heed popular sentiment will end up “on the wrong side of history.”