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One of her most famous books, The Year 1961, which chronicled her experiences during the Bay of Pigs invasion as a war correspondent at Playa Girón, Cuba, won the Casa de las Américas Award.
Mention at Premio Casa de las Américas, in Habana, Cuba in 2001, for the novel La Reina de América, "because it stands out as an intense writing regarding the established powers by the use of parody and irony," according to the panel of judges composed of Belén Gopegui (Spain), Andrés Rivera (Argentina), Mayra Santos Febres (Puerto Rico) and others
These include honorary doctorates from Universidad Autónoma de Sinaloa (1984), the Universidad Veracruzana (2004), the Universidad Autónoma Metropolitana (2007) and the Instituto Superior de Arte and the Casa de las Américas in Havana (2008).
Tavarez's artworks are shown at museums, art galleries and permanent collections worldwide, including the Museum of Modern Art in Santo Domingo, Casa de Las Americas in Havana, Cuba, The Housatonic Museum of Art in Connecticut, the Gallery of the Inter-American Development Bank in Washington DC, and the Museums of Modern Art in London, Mexico, Colombia, and Venezuela.