Fabry disease is a monogenic disease characterized by a deficiency or loss of the α-galactosidase A (GLA). The resulting impairment in lysosomal GLA enzymatic activity leads to the pathogenic accumulation of enzymatic substrate and, consequently, the progressive appearance of clinical symptoms in target organs, including the heart, kidney, and brain. However, the mechanisms involved in Fabry disease-mediated organ damage are largely ambiguous and poorly understood, which hinders the development of therapeutic strategies for the treatment of this disorder. Although currently available clinical approaches have shown some efficiency in the treatment of Fabry disease, they all exhibit limitations that need to be overcome. In this review, we first introduce current mechanistic knowledge of Fabry disease and discuss potential therapeutic strategies for its treatment. We then systemically summarize and discuss advances in research on therapeutic approaches, including enzyme replacement therapy (ERT), gene therapy, and chaperone therapy, as well as strategies targeting subcellular compartments, such as lysosomes, the endoplasmic reticulum, and the nucleus. Finally, the future development of potential therapeutic strategies is discussed based on the results of mechanistic studies and the limitations associated with these therapeutic approaches.