The paper outlines the current state in the model reduction of systems governing reacting flows by manifold methods. The main idea of such approaches is based on the fact that any reduced model defines a manifold of low dimension imbedded in the system composition/state space. In this respect the decomposition into relatively fast and slow motions due to multiple time scales present in the system is a crucial property of the reacting system. It allows the application of the geometrical framework of slow and fast invariant manifolds to model reduction. Recently developed approaches, namely, the so-called Reaction-Diffusion Manifolds (REDIMs) and Global-Quasi Linearization (GQL) are in the focus of this work. The methods extend and follow the well known ILDM method. The paper discusses both the theoretical basis of the approaches and detailed implementation schemes for studying, reducing and simulating the reacting flows systems. Simple yet containing all features of the reacting flows models of n-heptane/air and syngas/air systems are used to illustrate and verify the methods
