The world eagerly waits to find out as to Who Will Lead the Catholic Church Next? A Look at the Top Contenders for Pope. As the world awaits the opening of the papal conclave on May 7, attention turns not only to who the next pope might be, but what kind of man he must be. The task of choosing a successor to Pope Francis is both spiritual and deeply human, calling for discernment, wisdom, and humility from the 120 cardinals entering the Sistine Chapel.