Starch is a major food supply for humanity. It is produced in seeds, rhizomes, roots and tubers in the form of semi-crystalline granules with unique properties for each plant. Though the size and morphology of the granules is specific for each plant species, their internal structures have remarkably similar architecture, consisting of growth rings, blocklets, and crystalline and amorphous lamellae. The basic components of starch granules are two polyglucans, namely amylose and amylopectin. The molecular structure of amylose is comparatively simple as it consists of glucose residues connected through α-(1,4)-linkages to long chains with a few α-(1,6)-branches. Amylopectin, which is the major component, has the same basic structure, but it has considerably shorter chains and a lot of α-(1,6)-branches. This results in a very complex, three-dimensional structure, the nature of which remains uncertain. Several models of the amylopectin structure have been suggested through the years, and in this review two models are described, namely the "cluster model" and the "building block backbone model". The structure of the starch granules is discussed in light of both models.