α-Amylase catalyses the first step in the digestion of starch, a main source of carbohydrate in the human diet. Amylase present in human saliva was one of the first enzymes ever to be recognised but many puzzles remain about the molecular mechanisms involved in amylolysis of starch and even of the physiological role of the salivary amylase itself. Native starch granules represent a formidable challenge for attack from an enzyme in solution. Moreover the frequently reported differences in the susceptibility to amylolysis of starches from various botanical species, plus the changes that occur in starch structure and properties during domestic and commercial food processing means that studies of the enzymology of starch digestion can be challenging. We review the molecular properties of mammalian α-amylase including its genetics, and speculate on the role of salivary amylase in digestion of dietary starch. Also considered are enzyme kinetic approaches that have been used in vitro studies of amylase digestion of starches. Such studies can result in better understanding of reasons for the differences in glycaemic responses of humans following ingestion of different starch containing foods.