Background: With up to 200 published contributions, the GreenLab mathematical model of plant growth, developed since 2000 under Sino-French co-operation for agronomic applications, is descended from the structural models developed in the AMAP unit that characterize the development of plants and encompass them in a conceptual mathematical framework. The model also incorporates widely recognized crop model concepts (thermal time, light use efficiency and light interception), adapting them to the level o:f the individual plant. Scope Such long-term research work calls for an overview at some point. That is the objective of this review paper, which retraces the main history of the model's development and its current status, highlighting three aspects. (1) What are the key features of the GreenLab model? (2) How can the model be a guide for defining relevant measurement strategies and experimental protocols? (3) What kind of applications can such a model address? This last question is answered using case studies as illustrations, and through the Discussion. Conclusions: The results obtained over several decades illustrate a key feature of the GreenLab model: owing to its concise mathematical formulation based on the factorization of plant structure, it comes along with dedicated methods and experimental protocols for its parameter estimation, in the deterministic or stochastic cases, at single-plant or population levels. Besides providing a reliable statistical framework, this intense and long-term research effort has provided new insights into the internal trophic regulations of many plant species and new guidelines for genetic improvement or optimization of crop systems.