Mucopolysaccharidosis type III (MPS III) or Sanfilippo disease is an orphan inherited lysosomal storage disease and one of the most common MPS subtypes. The classical presentation is an infantile-onset neurodegenerative disease characterised by intellectual regression, behavioural and sleep disturbances, loss of ambulation, and early death. Unlike other MPS, no disease-modifying therapy has yet been approved. Here, we review the numerous approaches of curative therapy developed for MPS III from historical ineffective haematopoietic stem cell transplantation and substrate reduction therapy to the promising ongoing clinical trials based on enzyme replacement therapy or adeno-associated or lentiviral vectors mediated gene therapy. Preclinical studies are presented alongside the most recent translational first-in-man trials. In addition, we present experimental research with preclinical mRNA and gene editing strategies. Lessons from animal studies and clinical trials have highlighted the importance of an early therapy before extensive neuronal loss. A disease-modifying therapy for MPS III will undoubtedly mandate development of new strategies for early diagnosis.