For example, this week the head of the United Nations Population Fund, Thoraya Obaid, said she hoped the next pope would ease Catholic opposition to contraception as a way to combat the spread of AIDS.
The pressure to change policy on condoms is one of several challenges awaiting the next leader of the world's 1.1 billion Catholics.
But which issue is likely to get priority from the future pope depends on whom you ask.
The possible "clash of civilizations" between Christianity and Islam is certainly at the top of the list, says Robert Moynihan, a historian and editor in chief of the monthly magazine "Inside The Vatican."
"That's the fear that Christians have about Islam: that Islam does not want to admit that the force of persuasion alone is sufficient," Moynihan said. "They want to also use government power, they want to use military power, to force people to accept Islam. And the argument here is grave, profound, and intense. And Islam has to engage us on that argument."
And under the next pope, Moynihan added, Catholic leaders around the world are likely to play a key part in that emerging dialogue.
"Obviously, Islam is a factor now in Europe. Islam, of course, is in the Middle East. It's also a factor in India and into furthest Asia," Moynihan said. "And it's very much a factor all along the southern edge of the former Soviet Union and, therefore, Russia. So in each of these countries, if you want to talk about a relationship between Islam and Christianity, you're talking about a great interest for the cardinals and bishops of those countries. You're talking about men in each of those countries who could also be considered leaders in the possible dialogue between Christianity and Islam."
A few papal candidates, such as Nigerian Cardinal Francis Arinze, have made dialogue with Islam central to their mission.
Inter-religious violence in recent years has plagued Africa, where the Catholic Church is growing strongly despite competition for converts from Islam and Protestantism. Tens of thousands of people have died in fighting between Christians and Muslims in places such as Nigeria and Sudan.
David Shinn of George Washington University is a former U.S. ambassador to Ethiopia and Burkina Faso. He said the next pope will need to find a way to peacefully work with other religions as they seek to expand in Africa.
"The whole concept of inter-faith cooperation is something that needs to be highlighted," Shinn said. "I think as one looks to the election of a new pope, for example, and to the degree that Catholicism is important in Africa -- and it is very much a growing religion in Africa -- the role that Catholics can play, in addition to the Protestant groups and Muslims to try to dampen down the competition that is going on is frankly going to be in the interest of everyone."
As the next pope's gaze turns increasingly to the developing world, many experts believe the Catholic Church is likely to become more vocal about growing economic inequality and globalization.
Several Latin Americans in the running for the papacy, such as Honduran Cardinal Oscar Andres Rodriguez Maradiaga, have made the stand against economic injustice central to their message.
Rome-based Gerard O'Connell is a veteran Vatican-watcher and Catholic author.
"Many of them [the cardinals] see the gap between rich and poor, the impact of globalization, as an even greater [challenge than dialogue with Islam]," O'Connell said.
Still other experts, however, identify rampant secularism as the greatest challenge facing the Vatican's future leader.
Monsignor Romano Scalfi is an Italian priest who has spent nearly half a century working on dialogue with the Russian Orthodox Church. He believes that secularism -- or the view that religious considerations should be excluded from civil affairs or public education -- is in the process of "invading" former Soviet countries after having virtually conquered the affluent West.
Scalfi sees a future Catholic-Orthodox alliance as the best means for fighting secularism.
"We see ecumenism necessarily connected with our mission -- that is, we must help each other to overcome this skeptical, postmodern, cynical mentality which is the greatest threat to both the West and Russia," Scalfi said.
But still others see cynicism within the Catholic Church itself as the biggest challenge for a future pope to overcome.
U.S. victims of child abuse by Catholic priests this week accused the Vatican of "rubbing salt in an open wound" by allowing a cardinal tainted by the scandal to celebrate a memorial Mass for the pope.
Cardinal Bernard Law was forced to resign as archbishop of Boston in 2002 after taking the blame for allowing priests known to have sexually abused children to remain in the priesthood. Yesterday, Law presided over a Mass in memory of the late pope in Rome.
American Barbara Dorris, who says she was a victim of priestly sexual abuse as a girl, flew to Rome to voice her outrage.
''I think the problem is that the bishops, by hiding the molesters, by giving them fresh starts, by moving them, they allow them to have an incredibly long career, they don't go to jail," Dorris said.
On 18 April, 115 Catholic cardinals under the age of 80 will meet in a secret Vatican conclave tasked with choosing a new pope.
The conclave could last days, and the man finally chosen will have his hands full.
But besides Islam, secularism, globalization, and sex scandals, his biggest challenge might simply be filling the shoes of John Paul -- history's most widely traveled and arguably most popular pope.