[3] By the end of the decade, the Contemporary Arts Museum had outgrown the original 1950 facility, so the trustees raised funds to purchase a prominent site on the corner of Montrose and Bissonnet, where the new building, designed by Gunnar Birkerts, was built.

In addition, exhibitions of new Texas talent provided early venues for works of James Surls, John Alexander, and Luis Jimenez, among others.

[3] In the 1980s, the museum grew significantly, extending its sphere of influence with exhibitions that presented and toured surveys of installations for performance art; contemporary still-life painting; a group exhibition of work by Texas artists; and single-artist shows of artists like Ida Applebroog, Robert Morris, Pat Steir, Bill Viola and Frank Stella, as well as Texans Earl Staley, Melissa Miller and Vernon Fisher.

In addition, Director Linda L. Cathcart established Perspectives in the museum's lower gallery—a fast-paced series of exhibitions focusing on cycles of work by emerging and well-known artists that had not previously shown in Houston.

Major single-artist exhibitions at the end of the 20th century included Art Guys: Think Twice, Tony Cragg: Sculpture, Ann Hamilton: kaph, Richard Long: Circles Cycles Mud Stone, Nic Nicosia: Real Pictures, Introjection: Tony Oursler: 1976-1999, Lari Pittman, Robert Rauschenberg: A Retrospective, James Turrell: Spirit and Light, William Wegman: Paintings and Drawings, Photographs and Videotapes and Robert Wilson's Vision.

Single-artist shows have focused on a variety of media and have included "When One is Two: The Art of Alighiero e Boetti," William Kentridge, Uta Barth, and Juan Muñoz.