The men who might be pope VATICAN CITY - With the terrifying grandeur of Michelangelo's "Last Judgment" looming over them, senior leaders of the Roman Catholic Church will begin casting their ballots inside the Sistine Chapel on Tuesday to elect a successor to Benedict XVI, the first pope to resign in nearly 600 years. No one campaigns for the papacy, at least overtly; the surest way for a candidate to disqualify himself for the job is to let it be known that he wants it. But various names crop up repeatedly in discreet conversations as the 115 prelates eligible to vote try to figure out who among them is best placed to lead a historic but troubled institution that claims the allegiance of 1.2 billion people. PHOTOS: Sistine Chapel is readied for papal vote Whoever emerges from the conclave as the 266th pontiff will inherit a global church that is continuing to grow in far-off continents but waning in the Vatican's backyard; under challenge by other religions, notably Islam and evangelical Protestantism; unable to shake off a damaging scandal over clerical sexual abuse; and in the grip of a management crisis. Although there is no clear front-runner, the most frequently mentioned among the papabili - potential popes - come from a number of countries and have focused on various issues facing the church today. In picking a new pope, cardinals will be making a choice on which of the church's problems to tackle head-on. Below are four who reflect some of the aspects that the cardinals, the "princes" of the Catholic Church, must consider as they make their decision. From the moment Benedict announced his intention to retire, Angelo Scola has been considered a leading candidate to assume the throne of St. Peter. Scola, 71, is one of the senior Italians in the church hierarchy. He's archbishop of Milan, Italy's largest diocese, and former patriarch of Venice; the two cities have produced five popes between them within the last century. Though by no means united behind a single candidate, Italians make up a quarter of the cardinals who will select a new pontiff, more than double the number from the United States and more than those from all of Africa, Asia and Australia combined. But Scola's vision extends far beyond Italy. One of his primary interests has been dialogue and understanding between Christianity and Islam, which he promotes through a foundation, Oasis, that he set up while in Venice, historically a meeting place between East and West. Some commentators identify the need to respond to Islam, which is competing with the Catholic Church for hearts and minds in places such as Africa, as one of the most important issues facing the church. Benedict tried to reach out to Muslims but never overcame a blunder early in his papacy when he quoted a medieval writer who characterized Islam as an inherently violent religion. The gaffe ignited demonstrations across the Muslim world, during which an Italian nun in Somalia was killed. Few expect similar missteps from Scola, who has made frequent trips to the Middle East and is more of a natural diplomat than Benedict. The son of a truck driver, Scola is regarded as down to earth and accessible while also a man of deep learning. Scola has more experience in this sense, because he has traveled more. He knows Muslims through his foundation, particularly scholars," said Elio Guerriero, a writer and historian in Milan. The other religions, he says we must consider them as good and even an opportunity given by God to other people. Milan has experienced its own share of religious friction. For years, the local Muslim population has petitioned the city for permission to build a mosque but has met with hostility and, at times, overt prejudice from officials and backers of the anti-immigrant Northern League. The Catholic Church supports the Muslims' request, as does Scola, who was installed in Milan - often viewed as a papal training ground - a year and a half ago after serving in Venice. While Scola has fostered dialogue with other religions, his fellow Italian Gianfranco Ravasi has impressed some Vatican watchers with his engagement of atheists and agnostics and with his communications savvy. He keeps a blog, frequently updates his Facebook page and tweets with alacrity. Ravasi, 70, recently informed his Twitter followers that he was pondering a lyric, "Love is a losing game," by the late singer Amy Winehouse (his verdict on her songs: "lacerating musically and thematically"). At a Vatican synod in October on spreading the Gospel, participants said it was crucial for the next pope to be comfortable with social media as the church tries to deliver its message to nonbelievers in the digital age.