WHEN YOU FIRST catch sight of the Nomadic Museum, assembled on a pier on the Hudson River side of Manhattan, it looks like a place where somebody has been having some serious fun. How else do you describe 148 rectangular steel cargo containers, the kind you can see being lifted off ships at any port, all piled like giant toy blocks into walls 35 ft. high? This pier is no longer used for shipping—these days it's part of the New York City park system—but of late it has become an anchorage for an iconoclastic mind.

That would be the mind of Shigeru Ban, 47, the Tokyo-based architect known for his unexpected building materials, like bamboo and paper, and his ingenious systems of construction, like the one he devised for a home library in which the bookcases also served as walls to support the roof. A version of that system is in use at the Nomadic Museum, where some of the cargo-container walls will double as storage space. Two long rows of interior columns show off one of Ban's signature devices: hollow-core paper tubes so strong that they can carry heavy loads.

Ban designed this place for a single purpose: to enclose a traveling exhibition of 200 large photographs by the Canadian-born artist Gregory Colbert. When the show closes on June 6, the entire museum will be taken down, then rebuilt at each of the next stops, among them Los Angeles, Beijing and Paris. That's why it's called nomadic, though most of the shipping containers that form it won't actually be traveling. "You can rent them anywhere," Ban says. "But the roof structure we will ship from place to place."

Nomadic would also be a good word for many Japanese architects these days. In the first decades after World War II, the most forward-looking among them, including Kenzo Tange and Fumihiko Maki, secured international reputations without working much in the U.S. But in the past few years many of the most talked-about new American buildings have been produced by Japanese architects. First came the austere Pulitzer Foundation for the Arts in St. Louis, Mo., the work of Tadao Ando, 63, long one of Japan's biggest names. Next was his seraphic Modern Art Museum of Fort Worth, Texas, five thrusting cartons of glass and concrete that appear to float on an elliptical reflecting pool. Then last November the Museum of Modern Art (MOMA) in New York City reopened, intricately reconceived by Yoshio Taniguchi.

There is no such thing as "Japanese architecture," if what one means by that is a single aesthetic that could account for Ando's serene fields of velvety concrete, the delicate steel palisades of Taniguchi and Ban's witty-serious fabrications. But in the work of all three, Japanese traditions and aesthetic understandings are detectable, though always transmitted through a contemporary, international design vocabulary. "The materials of Modernism are steel, concrete and glass," says Ando. "These are materials that anybody can use, in the U.S. or Japan. But I think I can add to them a Japanese sensibility."

What's surprising is that it is Japanese architects—Ando and Taniguchi in particular—who have brought to the U.S. a reminder of the enduring virtues of classical Modernism, with its doctrine of clearly apparent forms and cleanly articulated lines and its deep suspicion of ornament, flourishes and superfluous gestures. At a time when the most talked-about global architecture starspeople like Frank Gehry, Zaha Hadid, Rem Koolhaas and Daniel Libeskindhave moved into a world of skewed angles, whiplash curves and highly irregular volumes, Ando and Taniguchi have stayed closer to the rule book of Modernism as taught by Le Corbusier and Ludwig Mies van der Rohe.

The architects, of course, prefer not to be cubbyholed in that way. "I've always been interested in movements," says Taniguchi, 67, "in what other people were thinking about, but I don't think about 'isms' in my own work. I'm not trying to work in a style of architecture. It's just my architecture." All the same, his indebtedness to classic Modernism is plain at his Gallery of Horyuji Treasures of the Tokyo National Museum. Completed six years ago, the gallery is part of a compound that also includes, just across the way, the Tokyo National Museum, designed by Taniguchi's late father Yoshiro. Though the younger Taniguchi discounts the idea, his building seems like a terse reckoning with two fathers, Mies and his own. The vertical tracery of its thin steel piers and the fine membrane of glass and steel that encloses the interior court are Miesian gestures carried out with a finesse that the old German himself only sometimes achieved. One of the most superbly poised buildings of the 20th century, the gallery recertifies one of Modernism's most basic intuitions—that when deployed by an elegant mind, the 90° angle can be more beautiful than the Apollo Belvedere.

For Ando, Mies is not the most important forebear. Ando's buildings, with their interlocking planes and contours and their lyrical use of concrete, owe more to Le Corbusier and the powerful concrete cylinders and spiritual aspirations of the great American architect Louis Kahn. When you come upon Ando's famous Church of the Light in the Osaka suburb of Ibaraki, completed in 1989, you understand that humble, heavy concrete has its spiritual side. (Does it matter that Ando was once a professional boxer?) The building is a masterpiece of vivid simplicity—a rectangle of bare concrete animated by the simple gesture of an oblique, freestanding fifth wall that slices the space at a 15° angle. Windows, slots and channel openings create a play of light in which Ando's wide wafers of concrete dematerialize. The light play culminates in a powerful gesture in the rear wall behind the pulpit. Two long, narrow openings meet to form a cross of pure sunlight that faces the congregation. "We don't need to use decoration," says Ando, "to make a warmhearted architecture."

As for Ban, his relation to Modernism, and for that matter to Japan, is complicated by his passion for everything from recyclable materials to the intricate curves of Alvar Aalto, the Finnish architect whose sensuous work was practically a rebuke to Mies and everything the hard-edged Miesian aesthetic represents. Ban is sometimes happy to invoke Japanese tradition. A pavilion he designed for Forest Park in St. Louis will feature a bamboo roof woven in a wickerwork pattern called ajiro in Japan, where it's often found in the ceiling of traditional houses. But like the Harvard-educated Taniguchi, he was schooled in the U.S. and draws his architectural language from all over. His Issey Miyake Design Gallery in Tokyo, where a bare rectangular interior is bordered on each of its long sides by large paper columns, invokes the peristyle hall of Greek temples in bare-bones Miesian terms—flat roof, glass-curtain wall. Yet at the same time, in the suave parabola formed by the rear rank of columns, there's also a hint of both Bernini's Baroque colonnades and Aalto's resonant curves. That's a lot of meaning in a little space.

To really understand any of the Japanese architects now commanding so much attention in the U.S., it helps to see their work in its own cultural context, amid the helter-skelter streetscapes in Tokyo or Osaka. Partly as a legacy of the Shinto sensitivity to processes and materials, Japan is a society famously devoted to beauty, a place where a supermarket sushi platter can be packaged as exquisitely as a Cartier brooch. But it's also one of the most heavily and hastily overbuilt nations in the world. World War II left many Japanese cities in ruins and opened the way to a postwar program of quick reconstruction. Then the Liberal Democratic Party, which has ruled Japan for most of the past 50 years, chose large-scale building projects as a linchpin of its program for economic revival. That helped produce the bubble economy of the '80s, which in turn led to even more construction, at least until the bubble burst. What it all left behind in many parts of Japan is a tightly clenched urban tissue, a cityscape so congested and haphazard, so outlined in neon and canopied with overhead power lines, that any zone of visual quiet is something to cherish.

Does this help explain the impulse toward lucidity and calm in Taniguchi and Ando, whose works have a magical composure even when they are set down in tumultuous places? Frank Gehry's buildings embrace, and then transfigure, the chaos of the modern world. Taniguchi's and Ando's absorb it and then settle it into the compelling order of their ideas. In his redesign of MOMA, for instance, Taniguchi draws in the surrounding city streets by way of ingeniously placed windows, slots and low walls. "I don't take the surroundings as a constraint. I take them as an element of the design," he says. "I enjoy it more when the conditions are more difficult, more complicated. That way I generate more creativity."

And more creativity is coming. Taniguchi is at work on a new museum in Houston for the Asia Society. Ando has designed a Philadelphia museum devoted to the artist Alexander Calder, and a large expansion of the Clark Art Institute in Williamstown, Mass. Ban, who is working on a new branch of the Pompidou Center in Metz, France, has also designed a house in Sagaponack, N.Y., part of a luxury development produced entirely by well-known architects. Also arriving in the U.S. these days is a generation of younger Japanese architects such as Kazuyo Sejima and Ryue Nishizawa, whose firm, SANAA, is responsible for the forthcoming home of the New Museum of Contemporary Art in Manhattan, an interesting stack of asymmetrically shifted boxes. That's not surprising: interesting design ideas have become one of Japan's most important exports. •