Laragh Cronin , Entertainment Editor May 4, Nonetheless, in Puebla, Mexico, traditional celebrations are still held. Military marches, recreations of the Battle of Puebla, and other festivities light up the city on May 5th. In the United States, particularly in densely populated Mexican-American areas, the day is celebrated with parades, mariachi music, Mexican folk dancing, and food. Lots and lots of food. Tostadas, quesadillas, tacos, churros, enchiladas… the list goes on.