Aims: The hereditary spastic paraplegias (HSPs) are a heterogeneous group of disorders characterized by spasticity in the lower limbs. We provide an overview of HSP with an emphasis on recent developments. Methods: A PubMed search using the term "hereditary spastic paraplegia" and "hereditary spastic paraparesis" was conducted for a period from January 2012 to January 2015. We discuss and critique the major studies in the field over this 36-month period. Results: A total of 346 publications were identified, of which 47 were selected for review. We provide an update of the common forms of HSP and include patient videos. We also discuss how next-generation sequencing (NGS) has led to the accelerated discovery of new HSP genes, including B4GALNT1, DDHD1, C19orf12, GBA2, TECPR2, DDHD2, C12orf65, REEP2, and IBA57. Moreover, a single study alone identified 18 previously unknown putative HSP genes and created a model for the protein interactions of HSP, called the "HSPome." Many of the newly reported genes cause rare, complicated, autosomal recessive forms of HSP. NGS also has important clinical applications by facilitating the molecular diagnosis of HSP. Furthermore, common genetic forms of HSP have been studied using new disease models, such as neurons derived from induced pluripotent stem cells. These models have been used to elucidate important disease mechanisms and have served as platforms to screen for candidate drug compounds. Conclusion: The field of HSP research has been progressing at a rapid pace. The challenge remains in translating these advances into new targeted disease therapies.The term "hereditary spastic paraplegia" (HSP) is applied to a group of inherited neurodegenerative disorders characterized by progressive spasticity and weakness in the lower limbs.There is marked genetic heterogeneity in HSP, with at least 55 genes and 72 loci identified thus far. The mode of inheritance can be autosomal dominant, autosomal recessive, X-linked, or maternal.