α-Glucosidases (AGases) and α-1,4-glucan lyases (GLases) catalyze the degradation of α-glucosidic linkages at the non-reducing ends of substrates to release α-glucose and anhydrofructose, respectively. The AGases belong to glycoside hydrolase (GH) families 13 and 31, and the GLases belong to GH31 and share the same structural fold with GH31 AGases. GH13 and GH31 AGases show diverse functions upon the hydrolysis of substrates, having linkage specificities and size preferences, as well as upon transglucosylation, forming specific α-glucosidic linkages. The crystal structures of both enzymes were determined using free and ligand-bound forms, which enabled us to understand the important structural elements responsible for the diverse functions. A series of mutational approaches revealed features of the structural elements. In particular, amino-acid residues in plus subsites are of significance, because they regulate transglucosylation, which is used in the production of industrially valuable oligosaccharides. The recently solved three-dimensional structure of GLase from red seaweed revealed the amino-acid residues essential for lyase activity and the strict recognition of the α-(1→4)-glucosidic substrate linkage. The former was introduced to the GH31 AGase, and the resultant mutant displayed GLase activity. GH13 and GH31 AGases hydrate anhydrofructose to produce glucose, suggesting that AGases are involved in the catabolic pathway used to salvage unutilized anhydrofructose.