By John L. Allen, Jr., CNN

Editor's note: John L. Allen Jr. is CNN’s senior Vatican analyst and a senior correspondent for the National Catholic Reporter.

Rome (CNN) - Every new leader gets a honeymoon period, and Pope Francis is smack dab in the middle of his. His gestures of simplicity and humility, set against the traditional grandeur of the papacy, have captured the imagination of the world.

Frankly, a whole team of PR wizards couldn’t have scripted a better start to his papacy.

At some point, however, charm alone won’t be enough, because Francis will have to turn to the heavy lifting of actually governing the world’s largest and most centrally organized religious body. Taking stock of where Catholicism stands today, he’s got his work cut out for him.

Four challenges loom especially large for the new pope.

First, two-thirds of the 1.2 billion Catholics on the planet today live in the Southern Hemisphere, a share projected to reach three-quarters by mid-century. If Catholicism was once a Western faith, associated with institutional power and privilege, its center of gravity is now in the developing world and its membership is strongest among the poor.

As the first pope from Latin America, and the first pope from outside Europe in more than 1,000 years, Francis carries the aspirations and expectations of all those non-Western Catholics with him into the papacy. They will expect him to be a tribune for their concerns: the inequities of a globalized economy, the carnage of war and violence, environmental degradation, and the perception that international affairs are stacked against the interests of smaller and poorer nations.

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