Until 2002, no representative structures existed for the glycoside hydrolase family 27 and clan D, which include the enzymes α-galactosidase (α-GAL, E.C. 3.2.1.22) and α-N-acetylgalactosaminidase (α-NAGAL, E.C. 3.2.1.49). Since then, four structures have been determined: α-NAGAL from chicken and α-GAL from rice, human, and Trichoderma reesei. This manuscript addresses the structure and function of the family 27 glycoside hydrolases, including the mechanism and substrate specificity. In humans, mutations in the α-GAL and α-NAGAL enzymes lead to the lysosomal storage disorders Fabry disease and Schindler disease, respectively, which are characterized by the incomplete degradation of carbohydrates with terminal α-galactose and α-N-acetylgalactosamine, respectively. The hundreds of mutations identified in Fabry and Schindler disease patients will be addressed in the light of the structures, revealing the atomic basis for the diseases.