Mixtures of solid reactants are usually ignited thermally, setting of a slow deflagration through the medium and progressive layers of material are heated by thermal conduction. When the system is shocked to pressures above its Hugoniot elastic limit, the solids behave like fluids and strong heating by compression also results. This leads to the propagation of the reaction front at velocities which are very high, even exceeding the sound velocity in the medium. Results are presented for these two forms of ignition. The chemical reaction can track the shock wave, completely converting reactants and propagating at velocities of several km/s.