Abstract Poly(lactic acid) is a biobased and compostable thermoplastic polyester that has rapidly evolved into a competitive commodity material over the last decade. One key bottleneck in extending the use of PLA is the control of its crystallinity. Understanding the crystallization behavior is particularly crucial to control PLA's degradation rate, thermal resistance as well as optical, mechanical and barrier properties. PLA crystallization has also been a particularly rich topic from a fundamental point of view because of the existence of the two enantiomeric forms of lactic acid that can be used to control the crystallization rate but also to form high melting point stereocomplex structures. This article presents an overview of the current understanding on the fundamentals of PLA crystallization in quiescent conditions and on the practical means to enhance its rate. Data from the abundant literature on PLA crystallization were compiled and analyzed to provide comprehensive relationships between crystallization kinetics and the main molecular structure characteristics of PLA. In addition, the most promising efforts in enhancing PLA crystallization kinetics through plasticization or heterogeneous nucleation were reviewed.