We first discuss the derivation of multicomponent flow models from the kinetic theory of polyatomic gas mixtures. We investigate in particular the structure of tranport fluxes the evaluation of multicomponent transport coefficients and the mathematical structure of transport linear systems. We then investigate the structure of the resulting system of partial differential equations and global existence results aroud constant equilibrium states with decay estimates. We also discuss anchored waves, that is, plane laminar flames with multicomponent transport and arbitrary complex chemistry. Finally, we discuss the numerical simulation of complex chemistry flame models.