Protesters gathered in Sana’a, and a violent year followed, in which government troops shot demonstrators and Saleh was wounded in a bomb attack. In February, 2012, he stepped down. Abdrabbuh Mansur Hadi, a diminutive bureaucrat who had served as Vice-President, began a two-year term. But the Houthis, who had participated in the uprising against Saleh, argued that power-sharing reforms endorsed by Hadi unfairly removed the northern regions’ access to the sea. They started pushing southward, out of their traditional homeland.

After Saleh left office, Abdulqader Hilal was appointed mayor of Sana’a. In 2014, when the Houthis began fighting Sunni Islamists on the outskirts of the capital, he led a negotiating team to enforce a truce that both sides had signed. “We just climbed the mountain to talk to them, and reminded them of what the agreement had been,” his son Hussein told me. “We were successful to stop this round of the war.”

A couple of months later, Saleh resurfaced, having performed a remarkable feat of political acrobatics: after leaving office, he had begun secretly collaborating with the Houthis. With his help, the Houthis invaded Sana’a, where, under the guise of fighting corruption, they began to install their leaders in key positions. After the Houthis took Sana’a, Hilal complained that their forces were stealing municipal equipment. When his car was stolen at a checkpoint, he briefly resigned. Hadi, who, though under house arrest, was still technically the head of state, refused his resignation. Hilal used his position to negotiate the release of high-profile officials who were being held by the Houthis. “We were expecting at any time that the Houthis might also keep my father from going outside his home,” Hussein said. “But that didn’t happen.”

In March, 2015, Hadi managed to escape, fleeing south. The Saudis, along with the United Arab Emirates, the Kingdom of Bahrain, and seven other Arab and African countries, began bombing Yemen, with the stated aim of restoring Hadi to the Presidency. In Washington and Riyadh, Saudi diplomats and soldiers assured their U.S. counterparts that the war would be over within six weeks. A U.N. Security Council resolution legitimatized their intervention.

Some officials in Washington were skeptical of the Saudis’ plans, however. “I think they had a slightly rosier interpretation of how quickly the military effort would be successful,” Nitin Chadda, who was an adviser on national security to the White House, told me. The Saudis had been “choreographing” their desire to take steps against the Houthis, because they were uncomfortable with the idea of an Iranian proxy on their border, he said. But the specific plans to attack Yemen were not communicated to the U.S. Within D.C. circles, Chadda said, “there was certainly frustration” that the Saudis had acted so quickly, without clearly defining their long-term objectives.

In May, Andrew Exum was appointed Deputy Assistant Secretary of Defense for Middle East Policy. “When I arrived, I sensed a lot of frustration,” he told me. The Administration was unsure about whether it wanted to be involved in the war. “Are we supposed to help the Saudis win or not? I don’t think we ever made our mind up there.”

Hilal decided to remain mayor of Sana’a, because he was concerned for the inhabitants, Hussein told me. “We’re talking about four million lives, we’re talking about people from everywhere in Yemen,” he said. “If he left office, things would be under the control of Houthis,” who had no experience running large metropolitan areas. In speeches to citizens, Hilal urged a kind of Blitz spirit: “Keep going for the glory of Yemen, for the ascendance of Yemen, for the stability of Yemen, for the revival of Yemen.”

The Saudis pounded Saada day and night, using bombs and cluster munitions, but they didn’t manage to dislodge the Houthis. Exum told me, “It was always going to be exceptionally difficult for the Saudis and the Emiratis to achieve a desired political outcome through the use of primarily air forces.” Apart from a couple of skirmishes, the Saudis used no ground troops. On May 8th, a spokesperson for the Saudi Army declared the entire city of Saada and a nearby area to be “military targets.” Within two months, air strikes had destroyed two hundred and twenty-six buildings in the city.

In November, 2015, despite American skepticism toward the Saudi war plan and evidence of heavy civilian casualties, the Obama Administration agreed to a giant weapons sale totalling $1.29 billion. The Saudis were authorized to buy seven thousand and twenty Paveway-II bombs. By the end of Obama’s Presidency, the U.S. had offered more than a hundred and fifteen billion dollars’ worth of arms to Saudi Arabia, the largest amount under any President, including warships, air-defense systems, and tanks.

The history of large-scale arms sales to Saudi Arabia dates to the late sixties, when U.S. weapons manufacturers realized that the Arab-Israeli conflicts of the era were being fought with Soviet and French arms. “For our defense companies, it was very frustrating,” Rachel Bronson, the author of “Thicker Than Oil,” a 2006 book on U.S.-Saudi relations, told me. The arms manufacturers lobbied the U.S. government, contending that arms sales were good policy. After all, U.S. experts would have to assemble and maintain the weapons, which could theoretically be dismantled if the Saudis were pursuing anti-U.S. policies. It was also good business: in 2016, the maintenance contract for the Royal Saudi Air Force’s two hundred and thirty F-15 fighter jets alone was worth $2.5 billion.

The Obama Administration saw Saudi Arabia both as a bulwark against terrorism and as a counterbalance to Iran. In “Kings and Presidents,” a book on the history of U.S.-Saudi relations, the former C.I.A. officer Bruce Riedel writes that “no president since Franklin Roosevelt courted Saudi Arabia as zealously as did Obama.” Not only did Obama authorize more arms sales than any other U.S. President; he visited Saudi Arabia more frequently than any of his predecessors. On his first trip to the Middle East, Riyadh was his first stop.

But, during the Arab Spring, the Saudis became angered by Obama’s failure to support their allies in Egypt, Tunisia, and Bahrain. The nuclear deal with Iran, signed in mid-2015, upset them further. “The Obama Administration was legitimately worried that a major fissure between the United States and Saudi Arabia could weaken the Iran deal,” Chris Murphy, a Democratic senator from Connecticut, who has opposed the U.S. government’s policy in Yemen, told me. “I think these arms sales were a way to placate the Saudis.”

The Obama Administration found itself entangled in the complexities of a war that involved so many regional players. The confusion extended to humanitarian concerns. Jeremy Konyndyk, at the time the director of USAID’s office of U.S. foreign-disaster assistance, told me that it often seemed as if the Saudis were thwarting efforts to get food to Yemen’s starving populace. Another former senior Administration official told me that the U.S. government spent four million dollars on cranes to unload relief ships at the Houthi-controlled port of Hodeidah, but the coalition, which had blockaded Yemen, did not allow the cranes into the country.

U.S. officials tried to help the Saudis improve their targeting. They eventually expanded a “no strike” list to include thirty-three thousand targets. “We broadened and broadened and broadened that list over time as the Saudis kept striking things that we would have thought they wouldn’t strike,” Konyndyk told me. The State Department sent an expert, Larry Lewis, to Saudi Arabia. When a civilian target was hit, Lewis wanted to help the Saudis implement ways of investigating the incident, to “avoid the same kind of thing happening again,” he said. Lower-ranking Saudis seemed pained by the casualties. “There was definitely a feeling that, of course we want to protect civilians, you know, we’re good Muslims,” Lewis said. The Saudi leadership was less concerned; as Lewis put it, from the rank of lieutenant colonel upward “there was less pressure for change.”