The alpha and beta phases of isotactic polypropylene form a pair of crystal phases which are characterized by the fact that the less stable beta phase has a faster growth rate than the more stable ct phase in a large central part of the crystallization range. Both phases share the same three-fold helical conformation, and growth transitions can take place between the two phases : thermal treatments needed to observe the transitions are described. The crystallographic relationship at the transition point is established with single crystals of the beta phase subjected to appropriate temperature jumps, and the possible structural origin of the faster growth rates is indicated. The growth transitions taking place at the upper and (mainly) lower ends of the crystallization range have a profound impact on the melting and recrystallization of the beta phase. These processes are reviewed, based on the extensive work of Varga (J. Thermal Analysis 1989, 35, 1891) and of Fillon et al. (J. Polym. Sci., Part B : Polym. Phys., 1993, 31, 1407).