Look around Europe and one leader stands above all the rest: German Chancellor Angela Merkel. In France, President François Hollande has given up the pretense that his country leads the continent. British Prime Minister David Cameron, triumphantly re-elected, is turning Britain into little England. Italian Prime Minister Matteo Renzi is preoccupied with his country’s comatose economy.

By contrast, in her 10 years in office, Merkel has grown taller with every upheaval. In the debt crisis, she began as a ditherer but in the end held the eurozone together; over Ukraine, she corralled Europeans into imposing sanctions on Russia (its president, Vladimir Putin, thinks she is the only European leader worth talking to), and over migration, she has boldly upheld European values, almost alone in her commitment to welcoming refugees.

It has become fashionable to see this as a progression from prudence and predominance to rashness and calamity. Critics assert that, with her welcoming attitude to asylum-seekers, Merkel has caused a flood that will both wreck Europe and, long before, bring about her own political demise. Both arguments are wrong, as well as profoundly unfair. Merkel is more formidable than many assume. And that is just as well: Given the European Union’s many challenges, she is more than ever the indispensable European.

Merkel’s predominance in part reflects the importance of Germany — the E.U.’s largest economy and mightiest exporter, with sound public finances and historically low unemployment. She is also the longest-serving leader in the E.U.

Her personal qualities count for much, too. She has defended Germany’s interests without losing sight of Europe’s; she has risked German money to save the euro, while keeping skeptical Germans onside, and she has earned the respect of her fellow leaders even after bruising fights with them. Most impressively (and alone among center-right leaders in Europe), she has done this without pandering to anti-E.U. and anti-immigrant populists. For all the E.U.’s flaws, she does not treat it as a punching bag, but rather as a pillar of peace and prosperity.

Merkel is far from perfect. She is not given to great oratory or grand visions. She can be both a political chameleon who adopts left-wing policies to occupy the center ground, and a scorpion who quietly eliminates potential rivals. Her natural caution has given rise to a German neologism, merkeln (“to Merkel,” or put off big decisions). Her timidity in handling the euro’s woes deepened the crisis unnecessarily; she has spurned the risk-sharing that the euro area needs to thrive.

Ironically, then, it is boldness, not timidity, that has brought Merkel the greatest challenge of her time in office. Her staunch refusal to place an upper limit on the number of refugees that Germany can absorb has caused growing consternation at home and criticism abroad. As German municipalities protest, her political allies are denouncing her and eastern European countries are accusing her of “moral imperialism.” With Willkommenskultur — a welcome culture — fading, there is even talk of her losing power.

The doubts are overblown. Critics are wrong to assume that Merkel is about to be toppled. Grumbling aside, she remains the dominant figure of her Christian Democratic Union (CDU). A recent poll found that 82 percent of CDU members approve of her leadership and that 81 percent want her to run for a fourth term as chancellor at the election due in 2017. The electoral math favors another CDU-led government. Merkel is unlikely to go unless she chooses to.

And the naysayers are wrong to suggest she has lost her way on migration. Quite the opposite. During the crisis, the Lutheran pastor’s daughter has found a forceful political and moral calling. Merkel did not cause the onrush of migrants, as her critics maintain. The migrants were coming anyway; she acted to avert a humanitarian disaster. Fences will not hold back the flow. Merkel can neither stop the wars that drive people out of their homes nor set the policies of the countries they pass through. Her critics offer no plausible alternative. Short of overturning international and European law, and watching refugees drown or die of exposure, E.U. countries must process the claims of asylum-seekers. The question is: Will the process be orderly or chaotic?

Under Merkel, a four-part policy is taking shape: unapologetically absorb refugees at home, share the burden across Europe and beyond, strengthen controls and the processing of asylum-seekers at Europe’s external borders, and negotiate with transit countries. This approach is principled and, in the long run, it is the only one that can work.

And there is no denying that the mass influx of refugees is aggravating many of Europe’s other looming problems: It is fraying relations between Germany and Eastern European countries just when solidarity is vital to contain Russia’s aggression; it is adding to the burdens of Greece, already crushed by years of austerity and never far from leaving the euro; it is bringing Britain’s exit from the E.U. closer, too, by giving voters more reasons to leave in Cameron’s promised in/out referendum, and it is stoking populism everywhere.

This is Europe’s biggest crisis in a generation. If integration once seemed inexorable, the pressing question now is how to stop the E.U. from fraying. Merkel did not cause this grim reality, but she is the continent’s best hope for dealing with it. It is in Europe’s best interests to help the chancellor rather than leave her to confront the crisis alone. After a decade in power, politicians usually retire, lose touch or are overthrown. But, without Merkel, it is hard to see Europe mastering its destructive forces.