The museum's building, a landmark work of 20th-century architecture designed by Frank Lloyd Wright, drew controversy for the unusual shape of its display spaces and took 15 years to design and build; it was completed in 1959.

Construction of the museum finally began in 1956 and took three years to complete. Much like the works of art that Solomon R. Guggenheim collected, this building is Modern in architectural design. It was built to challenge the “normal” way people view art with a building that almost wraps the viewer up in its atmosphere.

In 2019, The Guggenheim Foundation expected construction of the museum to be completed around 2023 and that the museum would include a center for art and technology, a children's education facility, archives, library and research center and a conservation laboratory.