GALA has been recognized for its contributions to the Hispanic arts at the local, national, and international levels. Artistic Director Hugo Medrano and resident Costume Designer Alessandra D'Ovidio were nominated for the 2000 Helen Hayes Award for Outstanding Director and Outstanding Costume Design, respectively, for their work in GALA's production of La Dama Boba. In 1981, GALA received one of the first Mayor's Arts Awards. In 1988, GALA received a Helen Hayes/American Express Award for outstanding leadership in theater.

U.S. tours include performances at New York's Public Theater and participation in the International Theater Festival of Miami, for which GALA was awarded the Miami Critics Association Award for Best Visiting Production. International appearances include Costa Rica, El Salvador, Venezuela, and Cuba with five different productions. In 1989, GALA was one of two U.S. companies invited to the International Theater Festival of San Jose for Peace in Costa Rica. In 1994, GALA performed Kiss of the Spider Woman to sold-out houses in the National Theater of El Salvador and participated in the International Theatre Festival of Central America. In 1997, GALA's production of Una visita inoportuna was presented at the Teatro San Martin in Caracas, Venezuela, and in 1998 GALA's production of Quintuples was presented at the Teatro Nacional in Havana, Cuba.

Hugo Medrano has been recognized on numerous occasions for his artistic excellence, including the Helen Hayes Award for Outstanding Lead Actor in a Resident Play (1994) and the Hispanic Achievement Award in Communications from Hispanic Magazine and AT&T (1994). Dahd Sfeir, a leading actress from Uruguay who starred in GALA's tango musical Mano a Mano, won the 1996 Helen Hayes Award for Best Actress in a Resident Musical Production. In 1998, Hugo and Rebecca Medrano were recognized by the Cultural Alliance of Greater Washington with its Founder's Award for their 22 years of achievement in bringing Spanish-language theater to the nation's capital. GALA was also the recipient of the 1998 Public Humanities Award by the Humanities Council of Washington, DC for its outstanding contributions to the city through promoting the public life of the humanities. In addition, Abel Lopez, Associate Producing Director, was honored with a 1991 Helen Hayes Award for Distinguished Community Service, a 1995 Lobby Award for Direction and Producing, and a 1996 Leadership Award by The Association of American Cultures

In January 2006, GALA co-founder and managing director Rebecca Read Medrano received the Mayor’s Arts Award for Excellence in Service to the Arts for her exemplary leadership, support and service to the development of the arts in the District of Columbia.