Drexler was born in Brooklyn[1] and attended the High School of Music and Art, and The Cooper Union studying architecture and served with the U.S. Army Corps of Engineers during the Second World War.
[2] After the war Drexler worked with the office of industrial designer George Nelson and was Architecture Editor of Interiors magazine.
Drexler joined the Museum of Modern Art in New York in 1951 as Curator of Architecture and Design and was promoted to Director of the Department in 1956 succeeding Philip Johnson.
During Drexler’s curatorship, MoMA played a central role in examining the work and reinforcing the reputations of twentieth-century architects, among them Frank Lloyd Wright, Le Corbusier, Richard Neutra, Marcel Breuer, and Ludwig Mies van der Rohe.
[9] In 1977, Drexler received the American Institute of Architects Medal for "vast contributions in documenting the art of architecture.