Originally built in 1850, Market Square opened as an open air market in 1852. For the rest of the 19th century, many Brownsville residents bought their fresh foods from the many stalls found in the Square. Even after being damaged by a hurricane in 1867, Market Square continued to operate as a market on the first floor and city offices on the second. By the 1940s, the stalls had been closed in, turning Market Square into just another enclosed building downtown.

In early 2009, Market Square was leased to the Brownsville Historicial Association. Thanks to the support of the Stillman Trust, Brownsville Community Improvement Corporation, and the City of Brownsville, Market Square became the home of BHA's collections and archives.

The vaults of Market Square house one of the largest South Texas photograph collections in the Rio Grande Valley. Additionally, the archives are home to numerous documents include the Frank Cushman Piece Papers and the A.A. Champion Collection.

The collections houses fine art, historical costumes, furniture, sculpture, and the extensive Backal art collection. Artists include Frederic Remington, Charles M. Russell, Armando Garcia Nunez, and Carlos Romero Orozco.