Sanfilippo syndrome or mucopolysaccharidosis III is a lysosomal storage disorder caused by mutations in genes responsible for the degradation of heparan sulfate, a glycosaminoglycan located in the extracellular membrane. Undegraded heparan sulfate molecules accumulate within lysosomes leading to cellular dysfunction and pathology in several organs, with severe central nervous system degeneration as the main phenotypical feature. The exact molecular and cellular mechanisms by which impaired degradation and storage lead to cellular dysfunction and neuronal degeneration are still not fully understood. Here, we compile the knowledge on this issue and review all available animal and cellular models that can be used to contribute to increase our understanding of Sanfilippo syndrome disease mechanisms. Moreover, we provide an update in advances regarding the different and most successful therapeutic approaches that are currently under study to treat Sanfilippo syndrome patients and discuss the potential of new tools such as induced pluripotent stem cells to be used for disease modeling and therapy development.