Mucopolysaccharidoses (MPSs) are known as rare genetic diseases which are caused by mutation in the enzyme heparin sulfate, which normally leads to degradation and accumulation of glycosaminoglycans in the cells. There are 11 types of MPSs, whereby neuropathy may occur in seven of them (MPS I, II, IIIA, IIIB, IIIC, IIID and VII). Accumulation of degraded heparin sulfate in lysosomes causes cellular dysfunction and malfunction of several organs. However, the exact molecular mechanism how protein degradation and storage leads to cellular dysfunction is not understood, yet. Nonetheless, several genetic and biochemical methods for diagnosis of MPSs are available nowadays. Here we provide an overview on known molecular basis of MPS in general, including enzyme defects and symptoms of MPS; however, the main focus is on MPS type III together with potential and perspective therapy-options.