Blind and depigmented fish belonging to the species Astyanax mexicanus are outstanding models for evolutionary genetics. During their evolution in the darkness of caves, they have undergone a number of changes at the morphological, physiological, and behavioral levels, but they can still breed with their river-dwelling conspecifics. The fertile hybrids between these two morphotypes allow forward genetic approaches, from the search of quantitative trait loci to the identification of the mutations underlying the evolution of troglomorphism. We review here the past 30years of evolutionary genetics on Astyanax: from the first crosses and the discovery of convergent evolution of different Astyanax cavefish populations to the most recent evolutionary transcriptomics and genomics studies that have provided researchers with potential candidate genes to be tested using functional genetic approaches. Although significant progress has been made and some genes have been identified, cavefish have not yet fully revealed the secret of their adaptation to the absence of light. In particular, the genetic determinism of their loss of eyes seems complex and still puzzles researchers. We also discuss future research directions, including searches for the origin of cave alleles and searches for selection genome-wide, as well as the necessary but missing information on the timing of cave colonization by surface fish.