The first significant progress in the genetic and pathogenic characterization of SCAs and HSPs occurred with the identification of the poly-Q repeat expansions as a frequent cause of ADCAs, of pathological GAA expansion in the FXN gene associated with Friedreich ataxia, and of mutations or major rearrangements located in the SPAST gene in association with pure HSP (SPG4). This evidence concerns the gene SPAST and Friedreich ataxia.