At the end of 19th century, Adolf von Strümpell and Sigmund Freud independently described the symptoms of a new pathology now known as hereditary spastic paraplegia (HSP). HSP is part of the group of genetic neurodegenerative diseases usually associated with slow progressive pyramidal syndrome, spasticity, weakness of the lower limbs, and distal-end degeneration of motor neuron long axons. Patients are typically characterized by gait symptoms (with or without other neurological disorders), which can appear both in young and adult ages depending on the different HSP forms. The disease prevalence is at 1.3-9.6 in 100 000 individuals in different areas of the world, making HSP part of the group of rare neurodegenerative diseases. Thus far, there are no specific clinical and paraclinical tests, and DNA analysis is still the only strategy to obtain a certain diagnosis. For these reasons, it is mandatory to extend the knowledge on genetic causes, pathology mechanism, and disease progression to give clinicians more tools to obtain early diagnosis, better therapeutic strategies, and examination tests. This review gives an overview of HSP pathologies and general insights to a specific HSP subtype called spastic paraplegia 31 (SPG31), which rises after mutation of REEP1 gene. In fact, recent findings discovered an interesting endoplasmic reticulum antistress function of REEP1 and a role of this protein in preventing τ accumulation in animal models. For this reason, this work tries to elucidate the main aspects of REEP1, which are described in the literature, to better understand its role in SPG31 HSP and other pathologies.