VATICAN CITY — With a puff of white smoke from the chimney of the Sistine Chapel and to the cheers of thousands of rain-soaked faithful, a gathering of Catholic cardinals picked a new pope from among their midst on Wednesday. The name of the new pope, the 266th pontiff of the Roman Catholic Church, by tradition would not be revealed until he appeared on a balcony on the front of St. Peter’s Basilica.

“It was like waiting for the birth of a baby, only better, " said a Roman man. A child sitting atop his father’s shoulders waved a crucifix.

The new pope inherits a church wrestling with an array of challenges that intensified during his predecessor, Benedict XVI — from a priest shortage and growing competition from evangelical churches in the Southern Hemisphere where most of the world’s Catholics live, to a sexual abuse crisis that has undermined the church’s moral authority in the West, to difficulties governing the Vatican itself.

Benedict abruptly ended his troubled eight-year papacy last month, announcing he was no longer up to the rigors of the job. He became the first pontiff in 598 years to resign. The 115 cardinals who are under the age of 80 and eligible to vote chose their new leader after two days of voting.

Before beginning the voting by secret ballot in the Sistine Chapel on Tuesday, in a cloistered meeting known as a conclave, the cardinals swore an oath of secrecy in Latin, a rite designed to protect deliberations from outside scrutiny — and to protect cardinals from earthly influence as they seek divine guidance.

The conclave followed more than a week of intense, broader discussions among the world’s cardinals where they discussed the problems facing the church and their criteria for its next leader.

“We spoke among ourselves in an exceptional and free way, with great truth, about the lights, but also about shadows in the current situation of the Catholic Church,” Cardinal Christoph Schönborn of Vienna, a theologian known for his intellect and his pastoral touch, told reporters earlier this week.

“The pope’s election is something substantially different from a political election,” Cardinal Schönborn said, adding that the role was not “the chief executive of a multinational company, but the spiritual head of a community of believers.”

Indeed, Benedict was selected in 2005 as a caretaker after the momentous papacy of John Paul II, but the shy theologian appeared to show little inclination toward management. His papacy suffered from crises of communications — with Muslims, Jews and Anglicans — that, along with a sex abuse crisis that raged back to life in Europe in 2010, evolved into a crisis of governance.

Critics of Benedict’s secretary of state, Cardinal Tarcisio Bertone, said he had difficulties in running the Vatican and appeared more interested in the Vatican’s ties to Italy than to the rest of the world. The Vatican is deeply concerned about the fate of Christians in the war-torn Middle East.

The new pope will also inherit power struggles over the management of the Vatican bank, which must continue a process of meeting international transparency standards or risk being shut out of the mainstream international banking system. In one of his final acts as pope, Benedict appointed a German aristocrat, Ernst von Freyberg, as the bank’s new president.

He will have to help make the Vatican bureaucracy — often seen as a hornet’s nest of infighting Italians — work more efficiently for the good of the church. After years in which Benedict and John Paul helped consolidate more power at the top, many liberal Catholics also hope that the next pope will also give local bishops’ conferences more decision-making power to help respond to the needs of the faithful.

The reform of the Roman Curia, which runs the Vatican, “is not conceptually hard, it’s hard on a political front but it will take five minutes for someone who has the strength. You get rid of the spoil system and that’s it,” said Alberto Melloni, the author of numerous books on the Vatican and the Second Vatican Council. The hard things are “if you want a permanent consultation of bishops’ conferences,” he added.

For Mr. Melloni, foreign policy and the church’s vision of Asia would be crucial to the next pope. “If Roman Catholicism was capable of learning Greek while it was speaking Aramaic, of learning Celtic while it was speaking Latin, now it either has to learn Chinese or ‘ciao,'” he said, using the Italian world for “goodbye.”

Ahead of the election of a new pope, cardinals said they were looking for “a pope that understands the problems of the Church at present” and who is strong enough to tackle them, said Cardinal Miloslav Vlk, the archbishop emeritus of Prague who participated in the general congregations but was not eligible to vote in a conclave.

He said those problems included reforming the Roman Curia, handling the pedophilia crisis and cleaning up the Vatican bank, which has been working to meet international transparency standards.

“He needs to be capable of solving these issues,” Cardinal Vlk said as he walked near the Vatican this week, adding that the next pope needs “to be open to the world, to the troubles of the world, to society, because evangelization is a primary task, to bring the Gospel to people.”

The sex abuse crisis remains a troubling issue for the church, especially in English-speaking countries where victims sued dioceses found to have moved around abusive priests.

On Wednesday, news reports in California showed that one cardinal elector, Cardinal Roger M. Mahony, the former archbishop of Los Angeles, the diocese and an ex-priest had reach a settlement of almost $10 million in four child sexual abuse cases, according to the victims’ lawyers.

Becoming pope also has a human dimension. In one of his final speeches as pope before he retired on Feb. 18, Benedict said that his successor would need to be prepared to lose some of his privacy.