Lysosomes and lysosomal enzymes play a central role in numerous cellular processes, including cellular nutrition, recycling, signaling, defense, and cell death. Genetic deficiencies of lysosomal components, most commonly enzymes, are known as “lysosomal storage disorders” or “lysosomal diseases” (LDs) and lead to lysosomal dysfunction. LDs broadly affect peripheral organs and the central nervous system (CNS), debilitating patients and frequently causing fatality. Among other approaches, enzyme replacement therapy (ERT) has advanced to the clinic and represents a beneficial strategy for 8 out of the 50–60 known LDs. However, despite its value, current ERT suffers from several shortcomings, including various side effects, development of “resistance”, and suboptimal delivery throughout the body, particularly to the CNS, lowering the therapeutic outcome and precluding the use of this strategy for a majority of LDs. This review offers an overview of the biomedical causes of LDs, their socio-medical relevance, treatment modalities and caveats, experimental alternatives, and future treatment perspectives.