He is known for having developed several theories of Modernist architecture, and for designing the master plan for the National Autonomous University of Mexico.
Villagán García was one of many young architects employed during the presidency of Alvaro Obregón (1920–24), following the Mexican Revolution 1910–1920.
Obregón's Minister of Public Education José Vasconcelos, who insisted that Mexican architecture carry meaning.
Villagrán García designed the huge National Stadium in Mexico City as a neo-Colonial structure, with a seating capacity of least 30,000.
However, the concrete also contained stone and volcanic tezontle, in a revival of the eighteenth-century style.