Pompe disease, also referred to as glycogenosis type II, is a rare, autosomal recessive disorder that results from the deficiency of the glycogen-degrading enzyme acid α-glucosidase. The classical form presents shortly after birth with muscle hypotonia, cardiac, and respiratory failure resulting in a fatal outcome. The late onset of Pompe disease has a very variable onset and disease presentation that often causes a delayed diagnosis. Until now enzyme replacement therapy with alglucosidase alfa is the only causative therapy option for Pompe patients that can slow down disease progression. However, uncertainty remains about the efficacy regarding survival and quality of life in Pompe patients under this very cost-intensive treatment. This paper provides a systematic review of the literature stressing different aspects of enzyme replacement therapy in infantile and late onset Pompe patients.