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Opposite the Brussels headquarters of NATO, across Boulevard King Leopold III, lies what the organization hopes to become.

Cranes rise up from a vast, fenced construction site into the gray Belgian sky. Billboards and signs on the outside tout what will emerge by 2015: a $1 billion-plus spaceship structure of glass and steel, open-plan offices and soaring footbridges. An airy, light-filled "agora" — that ancient meeting place of the public — will thread through the curved wings of the complex, replete with "areas for collaboration" and espresso bars. It is a building, NATO trumpets, fit for the needs of the 21st century.

But does the 21st century still need NATO? Back on the other side of the street, NATO's current home embodies the arguments of its critics. It is a fusty anachronism, a grim set of converted barracks built on an old airfield once developed by Hitler's Luftwaffe. In 1967, when NATO — then the West's military bulwark against the Soviet threat — shifted offices from Paris, the site was meant to be only temporary. But it has remained in its current state for 41/2 decades, a drab relic of another era, outlasting the Cold War and the disintegration of the USSR.

Inside NATO, the officials busying about in military green and bespoke blue speak only of the future. On May 20 in Chicago, the alliance will hold its largest-ever summit, bringing together heads of state from the 28 member countries and some 30 other national delegations. "NATO is as relevant as ever," its cobalt-eyed Secretary-General Anders Fogh Rasmussen tells me. "NATO is the strongest, most successful military alliance in the world. And now, faced with new security challenges, we have adapted."

Rasmussen notes the success of the alliance's intervention in Libya last year, when European leadership and American know-how combined to end the country's bloody civil war — and Muammar Gaddafi's 42-year rule. In Afghanistan — top on the summit agenda — NATO has led the fight against the Taliban. The alliance is keeping the peace in Kosovo, helping patrol the waters off Somalia's coast and monitoring the airspace above the Baltic Sea. Long past the Cold War, says Rasmussen, the alliance is now at "the hub of all global security."

That's the view from inside NATO. From the outside, the view is of an organization searching for a reason to exist. Far from representing the coordinated might of the West, NATO has come to symbolize its fragility. The financial crisis has shrunk already diminishing defense budgets in Europe, compelling some in Washington to question whether the other side of the Atlantic is keeping up its end of the NATO bargain. Skeptics point to the shortcomings of the operation in Libya: though the U.K. and France led the charge, nothing would have been accomplished without the U.S. doing all the heavy lifting behind the scenes, from running surveillance and flying the bulk of the sorties to providing munitions for NATO aircraft. The Europeans, after all, ran out of bombs.

Now, with the Obama Administration announcing a strategic "pivot" away from the Middle East and the Mediterranean toward rising challenges in the Pacific, NATO is becoming a relic of the past. For the first time in recent history, Asian military spending is predicted to exceed that of Europe this year, a trend that will only continue. With the Europeans set to wrangle over "smart defense" in Chicago — a NATO catchphrase for countries across the continent pooling military resources in an era of austerity — it's clear the U.S.'s traditional Western allies will be doing less with less.

And that may be inevitable. "The geopolitical balance is becoming increasingly driven by questions of economy, not security," says Ian Bremmer, author of Every Nation for Itself: Winners and Losers in a G-Zero World.

Faced with slumping economies and citizens weary of the war in Afghanistan, NATO governments are scrambling to wind down their involvement there as inconspicuously as possible. Once the mission draws down by 2014, it's hard to imagine the alliance embarking on an operation of that scale ever again. NATO's impotence in the face of Syria's bloody civil conflict — officials in Brussels insist they have not done contingency planning for an intervention — indicates that the Libya campaign was the exception that proves no rule.

Defenders of NATO claim that the alliance, as a group of like-minded democracies, has at the very least an ideological role. But other rising democracies, such as India and Brazil, have little interest in getting enmeshed in an organization created during the Cold War to buttress U.S. foreign policy. Bold rhetoric and a fancy new home won't change the fact that, ultimately, the challenge facing NATO is not that of a clear external threat, but the very lack of it.

• Ishaan Tharoor
• As NATO meets in Chicago, is the world's biggest military alliance fading into obsolescence?