In order to reduce computational resources, two main routes are generally followed to model the detailed dynamics and structure of laminar and turbulent flames: chemical reduction techniques and laminar flamelet models. In the last few decades an alternative method has been proposed and developed referred to as the Flamelet Generated Manifold (FGM ) method. The method is based on the laminar flamelet equations but applied similarly as the ILDM reduction method, i.e. by solving transport equations for a variable number of controlling variables. FGM is therefore considered as a combination of the two methods. Advantage of FGM compared to ILDM is that diffusion processes, which are important near the interfaces of the reaction layer and the outer inert zones, are taken into account. This leads to a very accurate method that uses less controlling variables than ILDM. Meantime, FGM has been developed further step-by-step and applied in a number of fundamental flame studies to model laminar premixed, non-premixed as well as partially-premixed flames, but also to model turbulent combustion in combination with DNS, LES and RANS models for the flow field. In the presentation, the basic formalisms will be derived and applied to different combustion models in well defined laboratory burner systems, and the performance of the model will be compared with detailed models and experiments. More recently, the FGM model has also been applied on diesel spray modeling in engine related studies as well as to gas turbine related systems. Some typical results will be shown and again compared with experiments.