Hereditary spastic paraplegias (HSP) are a heterogeneous group of motor neurodegenerative disorders that have the core clinical presentation of pyramidal syndrome which starts typically in the lower limbs. They can present as pure or complex forms with all classical modes of monogenic inheritance reported. To date, there are more than 100 loci/88 spastic paraplegia genes (SPG) involved in the pathogenesis of HSP. New patterns of inheritance are being increasingly identified in this era of huge advances in genetic and functional studies. A wide range of clinical symptoms and signs are now reported to complicate HSP with increasing overall complexity of the clinical presentations considered as HSP. This is especially true with the emergence of multiple HSP phenotypes that are situated in the borderline zone with other neurogenetic disorders. The genetic diagnostic approaches and the utilized techniques leave a diagnostic gap of 25% in the best studies. In this review, we summarize the known types of HSP with special focus on those in which spasticity is the principal clinical phenotype ("SPGn" designation). We discuss their modes of inheritance, clinical phenotypes, underlying genetics, and molecular pathways, providing some observations about therapeutic opportunities gained from animal models and functional studies. This review may pave the way for more analytic approaches that take into consideration the overall picture of HSP. It will shed light on subtle associations that can explain the occurrence of the disease and allow a better understanding of its observed variations. This should help in the identification of future biomarkers, predictors of disease onset and progression, and treatments for both better functional outcomes and quality of life.