In the present review, using an integrated approach based on the experimental and theoretical study of the processes of thermal decomposition and combustion of practically important polymers, such as polymethyl methacrylate, polyethylene, and glass-fiber-reinforced epoxy resin, the features of the mechanism for reducing the combustibility of these materials with phosphorus-containing flame-retardants (FR), as well as graphene, are identified. A set of original experimental methods was developed and applied that make it possible to study the kinetics of thermal decomposition and the thermal and chemical structure of the flames of the studied materials, including those with FR additives, as well as to measure the flame propagation velocity, the mass burning rate, and the heat fluxes from the flame on the surface of a material. Numerical models were developed and tested to describe the key parameters of the flames of the studied polymeric materials. An analysis of the experimental and numerical simulation data presented showed that the main effect of phosphorus-containing fire-retardants on reducing the combustibility of these materials is associated with the inhibition of combustion processes in the gas phase, and the effect of adding graphene manifests itself in both gas and condensed phases.