Fabry disease (FD) is a rare X-linked lysosomal storage disorder caused by mutations in the α-galactosidase A (AGAL/GLA) gene. The lysosomal accumulation of the substrates globotriaosylceramide (Gb3) and globotriaosylsphingosine (lyso-Gb3) results in progressive renal failure, cardiomyopathy associated with cardiac arrhythmia, and recurrent strokes, significantly limiting life expectancy in affected patients. Current treatment options for FD include recombinant enzyme-replacement therapies (ERTs) with intravenous agalsidase-α (0.2 mg/kg body weight) or agalsidase-β (1 mg/kg body weight) every 2 weeks, facilitating cellular Gb3 clearance and an overall improvement of disease burden. However, ERT can lead to infusion-associated reactions, as well as the formation of neutralizing anti-drug antibodies (ADAs) in ERT-treated males, leading to an attenuation of therapy efficacy and thus disease progression. In this narrative review, we provide a brief overview of the clinical picture of FD and diagnostic confirmation. The focus is on the biochemical and clinical significance of neutralizing ADAs as a humoral response to ERT. In addition, we provide an overview of different methods for ADA measurement and characterization, as well as potential therapeutic approaches to prevent or eliminate ADAs in affected patients, which is representative for other ERT-treated lysosomal storage diseases.