Among the chromosome fragility-associated human syndromes that present cancer predisposition, Fanconi anemia (FA) is unique due to its large genetic heterogeneity. To date, mutations in 21 genes have been associated with an FA or an FA-like clinical and cellular phenotype, whose hallmarks are bone marrow failure, predisposition to acute myeloid leukemia and a cellular and chromosomal hypersensitivity to DNA crosslinking agents exposure. The goal of this review is to trace the history of the identification of FA genes, a history that started in the eighties and is not yet over, as indicated by the cloning of a twenty-first FA gene in 2016.