After all the controversy, lawsuits, and delays in building the New Acropolis Museum in Athens, it will no doubt seem churlish to point out that the $180 million museum, designed by Bernard Tschumi Architects, is not the firm’s most spectacular work. It lacks the lyrical grace of the stainless-steel-and-concrete Zenith concert hall in Rouen or the finesse of the shimmering, perforated-steel Vacheron Constantin headquarters in Geneva, Switzerland, to name two. The dour mien of the New Acropolis Museum, with its sharp angles, black-fritted glass (except for a small section of the south wall), and less-than-perfect concrete work evokes High Modernist commercial American buildings of the 1970s.

That said, the interior of the museum provides a stunning setting for the Parthenon marbles displayed on its top floor. Here, museumgoers first encounter staggering views of the ancient, 5th-century B.C. temple through an expansive, 276-foot-long glazed wall facing north. Indeed, the elegant design of many of the museum interiors, and especially the Parthenon Gallery, makes a convincing case for the Elgin Marbles—removed by Lord Elgin between 1801 and 1810, when he was an ambassador from Great Britain to the Ottoman Empire—to be returned by the British Museum to Greece, and joined with the surviving originals. Increasingly over the years, Greece has argued vociferously for the return of the marbles to Athens: Since 1975, the government has planned to replace its smaller, 19th-century museum tucked into a corner of the Acropolis with a much larger structure that could adequately house the priceless treasures. It took four competitions to arrive at the final scheme, located in the historic, residential Makriyianni district. (The third, won in 1989 by Italian architects Manfredi Nicoletti and Lucio Passarelli, was aborted after archaeological remains from the 6th-century B.C. to the 5th-century A.D. were found on the 5.68-acre site.)

When Tschumi and his associate architect Michael Photiadis entered the fourth competition in 2000, a jury that included Santiago Calatrava and author/architect Dennis Sharp selected their scheme over those by Daniel Libeskind, Arata Isozaki, and nine other architects. Even though the program called for building over the ruins, the extensiveness of the excavations required the winning project to be readjusted in 2002, and any thought of its being finished for the 2004 Olympics in Athens was dismissed. The museum finally opened in June 2009, unsurprisingly accompanied by a chorus of impassioned pleas by Greek officials that the Elgin Marbles be brought back to this new home.

Tschumi’s concept for the 226,000-square-foot museum called for stacking three rectangular volumes on top of each other. The first two floors conform to the street grid, while the third rectangle is rotated 23 degrees from them to align its Parthenon Gallery with the ancient building itself. The gallery displays both surviving marble reliefs owned by the Greek government, along with plaster casts that the British Museum made of the original Lord Elgin trove. Visitors arriving at this third-floor outlook can behold the breathtaking majesty of the Parthenon high on its stony ramparts, and then direct their gaze back to the interior core where the marbles (real and fake) are arrayed from the original Ionic Panathenaic frieze sculpted by Phidias, of which 335 feet still exist from the 552-foot-long original. Tschumi placed the panels according to their sequence on the upper wall of the cella (the inner sanctuary of the Parthenon) girded by a pteroma, or corridor, and the Doric columns. Here, too, you find the metopes, cruder in relief, that once alternated with triglyphs in the entablature above the temple’s perimeter columns. Here they are held between steel columns (sheathed in a gleaming stainless steel), which are spaced to follow the original 14-feet-on-center placement of the slightly wider ones in the Parthenon.

To get to the Parthenon Gallery, visitors follow a processional path ingeniously devised by Tschumi that takes them through the various levels of the museum­—and through layers of time. They see arrayed before them objects arranged in chronological order that belong not only to the Periclean temple, but to other temples on the Acropolis as well. The museum circulation, an angular spiral, begins at the first level, where a fritted-glass floor and a curved void under the entrance canopy reveal the excavated ruins below. Proceeding inside, museumgoers find the Gallery of the Slopes, an inclined ramp also fitted with a glass floor over the excavations and flanked by vitrines containing artifacts from the lives of the ancient Greeks who resided on the Acropolis’s hillsides. A short stair ahead leads to another level (Level + 1), where fragments from the pediment of the 6th-century B.C. Hecatompedon—the Acropolis temple devoted to Athena that existed before the Parthenon—terminate this axial path, albeit without the punch one might expect: The angled stainless-steel brise-soleil backdrop distracts the eye from the ancient marble pedimental sculptures.

Proceeding to the south side of the building, visitors find themselves in an awe-inspiring, monumental, 33-foot-high hall. Here, 6th-century kouros (youth) and kore (maiden) statues from the Archaic period stand on marble pedestals among a forest of concrete columns. The design team’s brilliant juxtaposition of columns and freestanding statues emphasizes their differences in scale, and provides an effective spatial play for visitors meandering through the space. The processional path continues around to the west side of the museum, where museumgoers encounter the Caryatids from the Erechtheum (circa 405 B.C.)—one of which is still in the British Museum. Finally, the museumgoers ascend the escalator to the top level—the main event— where the Parthenon Gallery wraps around four sides of the concrete core of the museum unfolding views of Athens—and the Acropolis.

Here, the mottled mix of real and fake Parthenon marbles argues the case for repatriation better than if the museum had omitted the casts: You want to see all authentic surviving pieces put in place. And it is strikingly easy to spot the missing ones, owing to the disparity between the white plaster casts and the tan marble sculptures.

Having understood the raison d’être for the museum, you might think you’re done—but more awaits. A downward progression takes museumgoers to the Post-Parthenon and Roman exhibits on the west and north side of Level + 1 gallery, and on to the ground level. If you are a hurried, been-there, done-that tourist, look for the elevators.

The actual problem with the architecture of the museum hardly dwells in a very directed processional path: It has more to do with the exterior. If the circulation and the careful installations prove to be the museum’s strong points, its elevations are the weakest. Like much modern architecture—and unlike the Parthenon—they seem as if Tschumi wanted to build the diagram and call it a day. Having each floor’s elevation differ in the handling of light, energy load, and view (through varied curtain walls, steel fins, and precast panels) has created a disjointed whole. Tschumi rightly resisted pressure to use the Parthenon’s Classical vocabulary, even if dividing the building horizontally into three parts may seem to be an abstracted gesture toward the tripartite division of the Classical column, with its base, shaft, and capital. But these variegated stacked rectangles of reinforced concrete supplemented by precast panels, plus the Parthenon Gallery, which is cranked and cantilevered from a steel frame, are unresolved as an ensemble. While the top rectangle is the best, owing to its impeccable double-facade curtain-wall system that cuts solar load and helps ventilation, from the outside it still looks like the box the Parthenon came in.

The rotation of that top creates odd roof wedges, repeated in the angular entry canopy and the stainless-steel fins. Whereas the glass-mullioned curtain wall and the metal fins give many surfaces a certain luminosity and sheen, the black frit of the curtain wall is too grim from most viewpoints. (Granted, frit is needed for solar protection, but black?) In addition, the Herculean columns resting on smaller clusters of below-grade piloti (to carry the weight of the structure by carefully negotiating footholds among the ruins) create an odd lack of coherence between pieces and parts, proportions and scale. The biomorphic shapes of the cutouts over the ruins may help in viewing the archaeological excavations, but do add to the jarring gestalt.

The whole is hardly helped by the mediocre craftsmanship of the concrete. When Tschumi used concrete in France, it looked like the ghost of Auguste Perret had guided the pour. In this case, any New York contractor might be credited with calling the shots. This is a far cry from what Callicrates and Ictinus did with marble up the hill. Nevertheless, the strength and drama of the galleries, especially those devoted to the Archaic period and the Parthenon marbles, create a stunning home for these precious fragments of Western civilization. The Parthenon Gallery’s space and majesty alone makes the strongest argument for returning the Parthenon marbles to their proper setting.