The museum's primary collection contains works by renowned painters including El Greco, Diego Velázquez, Ribera, Murillo, Goya, Miró, Sorolla, Dalí and Picasso.

The museum currently occupies a neo-Palladian building designed by Chicago-based architects Hammond Beeby Rupert Ainge, which was completed in 2001 and dedicated in a ceremony that included King Juan Carlos I and Queen Sofía of Spain.

The museum's collection of Spanish art and the galleries for its display were a gift to Southern Methodist University from Algur H. Meadows, a Dallas businessman and founder of the General American Oil Company of Texas.

During the 1950s business took Meadows frequently to Madrid, where repeated visits to the Prado Museum inspired what would become a lasting interest in the art of the Spanish Golden Age.

This fruitful partnership has resulted in a comprehensive campaign of conservation, the support of scholarly research of the collection, and a number of important acquisitions, particularly in the areas of medieval, Baroque, and 20th-century art.