The mathematical modeling of chemically reacting mixtures is investigated. The governing equations, that may be split between conservation equations, thermochemistry and transport fluxes, are presented as well as typical simplifications often encountered in the literature. The hyperbolic-parabolic structure of the resulting system of partial differential equations is analyzed using symmetrizing variables. The Cauchy problem is discussed for the full system derived from the kinetic theory of gases as well as relaxation towards chemical equilibrium fluids in the fast chemistry limit. The situations of traveling waves and reaction-diffusion systems is also addressed.