Hereditary spastic paraplegia is an inherited, progressive paralysis of the lower limbs first described by Adolph Strümpell in 1883 with a further detailed description of the disease by Maurice Lorrain in 1888. Today, more than 100 years after the first case of HSP was described, we still do not know how mutations in HSP genes lead to degeneration of the corticospinal motor neurons. This review describes how patient-derived stem cells contribute to understanding the disease mechanism at the cellular level and use this for discovery of potential new therapeutics, focusing on SPAST mutations, the most common cause of HSP.