Even as it embraced nature, Wright's design also expresses his unique take on modernist architecture's rigid geometry. The building is a symphony of triangles, ovals, arcs, circles, and squares. Forms echo one another throughout: oval-shaped columns, for example, reiterate the geometry of the fountain and the stairwell of the Thannhauser Building. Circularity is the leitmotif, from the rotunda to the inlaid design of the terrazzo floors.

The meticulous vision took decades to be fulfilled. Originally, the large rotunda was to be accompanied by a small rotunda and a tower. The small rotunda (or monitor building, as Wright called it) was intended to house apartments for Rebay and Guggenheim but instead became offices and miscellaneous storage space. In 1965, the second floor of the building was renovated to display the museum's growing permanent collection, and with the restoration of the museum in 1990–92, it was turned over entirely to exhibition space and rechristened the Thannhauser Building in honor of one of the most important bequests to the museum.

Wright's original plan for the tower—artists' studios and apartments—went unrealized, largely for financial reasons. As part of the restoration, a 1968 office/art-storage annex (designed by Wright's son-in-law William Wesley Peters) was replaced by the current structure, designed by Gwathmey Siegel and Associates Architects, LLC. This tower provides four additional exhibition galleries and, some thirty-five years after the initiation of construction, completed Wright's concept for the museum. In 2001, the Sackler Center for Arts Education opened to the public. Located just below the rotunda, this 8,200-square-foot education facility includes the Peter B. Lewis Theater, part of Frank Lloyd Wright's original architectural design for the building.

Some people, especially artists, criticized Wright for creating a museum environment that might overpower the art inside. "On the contrary," he wrote, "it was to make the building and the painting an uninterrupted, beautiful symphony such as never existed in the World of Art before." In conquering the static regularity of geometric design and combining it with the plasticity of nature, Wright produced a vibrant building whose architecture is as refreshing now as it was 40 years ago. The Solomon R. Guggenheim Museum is arguably Wright's most eloquent presentation and certainly the most important building of his late career.

—Matthew Drutt