Poly[(R)-3-hydroxybutyrate] (PHB) is the first produced and most studied polyhydroxyalkanoate (PHA), a class of polymers that can be synthesized by a variety of bacteria through fermentation. PHB, and with it most PHAs, is produced in vivo, contrarily to all other types of bio-based and biodegradable polymers that are attained by chemical reactions, like polycondensation or ring-opening polymerization. The in vivo polymerization leads to a number of special features, like the absence of catalyst residues and other impurities typically present in synthetic polymers, which can promote crystal nucleation. Moreover, PHB has a perfectly isotactic structure with all chiral carbon atoms in (R)-configuration. These peculiarities make PHB a model compound for the study of polymer crystallization; hence its crystallization behavior has received considerable attention over the years. The main properties of the polymer are presented and discussed, together with literature data on crystal structure and morphology of PHB. This is followed by in-depth analysis of the crystallization kinetics, including both the primary crystal nucleation and crystal growth. Secondary crystallization is also discussed, as it largely affects time dependent properties of molded PHB products, which progressively becomes brittle upon storage: the glass transition of PHB is around 0°C; hence at room temperature PHB amorphous chains have sufficient mobility to continue to crystallize, which in turn implies also vitrification of part of the amorphous chains coupled with the crystals, the rigid amorphous fraction (RAF). The influence of the RAF on crystallization of PHB is also discussed, since its vitrification during crystallization can hinder or even stop further crystal growth. The analysis of the crystallization behavior of PHB is completed by a thorough discussion of melting of PHB crystals, which also presents a number of notable features.