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.

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.

It began at the Meadows (13 December 2013 – 19 April 2014), then traveled to the San Diego Museum of Art (30 May – 26 August 2014) and Fundación MAPFRE in Madrid (23 September 2014 – 11 January 2015).