Yearning for leadership

March 20, 2014, 3:50 PM UTC

When a reformer sweeps through an institution more forcefully in just a year than any other in memory — and when that institution is some 2,000 years old and the largest organization on earth — he draws attention, admiration, and wonder. That’s why Pope Francis leads our inaugural list of the World’s Greatest Leaders, and why he was proposed more often by our nominators than any other candidate. Reforming the scandal-plagued Vatican bank, finally beginning to address the child sexual abuse scandal, shaking up the Vatican’s self-absorbed bureaucracy, setting a striking new tone through his personal example of modesty and inclusiveness — this is what a great leader does.

The world yearns for such leadership. Only 21% of those surveyed globally say they trust business leaders to “make ethical and moral decisions,” says the Edelman communication firm’s latest Trust Barometer; only 15% trust government leaders to do so. Maybe the problem is that as the world changes and challenges multiply faster, delivering great leadership is getting harder. We hear it from others and feel it ourselves: The leaders we need are frequently just not there. So we went in search of them.

The great news is, we found scores of extraordinary individuals — so many that it was hard to winnow down our selections to just 50. (We’ve included one three-way tie.) We found inspiring, impressive leaders in every field of endeavor across the globe. On six continents — in business, government, the military, philanthropy, religion — we identified men and women, young and old, who are leading the way people want to be led. Crave to be led. Some, like the Pope, are world famous; many you’ve never heard of.

MORE: The World’s 50 Greatest Leaders

Choosing them necessarily required judgment. “There is no formula for leadership,” says Leading Marines, a book that all U.S. Marines are required to read, and on this we may regard the Marines as authoritative. So we cast our net broadly to include leaders of strictly hierarchical organizations (including the Marines) as well as others whose followers may owe no formal duty to the leader but who look to that person for inspiration and guidance. Some of our leaders, such as Alibaba chief Jack Ma (No. 16), are visionaries who inspire others to follow them toward a goal only they may see clearly; others, like Ford CEO Alan Mulally (No. 3), rescue institutions in trouble. Some, such as sports coaches, compete and win; others, like social entrepreneurs, cooperate and give.

We have drawn a distinction between leaders and people who are admirable and powerful but who are not transformative leaders. Simply running a large organization or serving in an influential role does not meet the threshold to be on this list. All candidates had to be currently active; thus no retirees or recently deceased great leaders, such as Nelson Mandela. We asked several noted leadership experts to suggest candidates, combined their ideas with others turned up by Fortune reporters, and vetted our nominees with experts in their respective fields. Then we made our final judgments based on the reality that while leadership can’t be measured, we all know it when we see it.

“A leader’s job is to define reality and give hope,” says American Express CEO Ken Chenault (No. 18). In an environment that often feels leader-deficient, our list exposes the reality that the world is actually filled with knockout leaders. And does it ever give hope.

This story is from the April 7, 2014 issue of Fortune.