His recent solo exhibitions include: Museum of Art of Lima (MALI), Lima; Sikkema Jenkins & Co., New York; Baltimore Museum of Art, Baltimore. Earlier presentations include: Pérez Art Museum, Miami; University Ga- lleries of Illinois State University; Marfa Contemporary, Texas; Fleming Museum, University of Vermont; P.S.1 Con- temporary Art Center, New York; and Museum of Contemporary Art, Miami; among others.

His recent group exhibitions include Whitney Museum of American Art, New York; Orlando Museum of Art; Nasher Museum of Art, Durham; SITElines Santa Fe; and Guggenheim Museum, New York; among others. His work has also been presented in major international biennials and triennials including the 13th Havana Biennial; 12th Havana Biennial; Whitney Biennial; San Juan Triennial; and 50th Venice Biennale (2003); among others.

William Cordova’s work is held in public and private collections including Solomon R. Guggenheim Museum, New York; Whitney Museum of American Art, New York; Walker Art Center, Minneapolis; New Museum, New York; The Menil Collection, Houston; Institute of Contemporary Art (ICA), Boston; Museum of Contemporary Art, Miami; Pérez Art Museum Miami (PAMM); Modern Art Museum of Fort Worth; American Academy, Berlin; Deutsche Bank, New York; Harvard University, Cambridge; Yale University, New Haven; Seattle Art Museum; and Museo de Arte de Lima; among others.

In 2008 he was artist-in-residence at Artpace, San Antonio, Texas.