Recent experimental and theoretical advances in the understanding of high-pressure, high-temperature chemical kinetics are used to extend the nonequilibrium Zeldovich-von Neumann-Doring (NEZND) theory of self-sustaining detonation in liquid and solid explosives. The attainment of vibrational equilibrium behind the leading shock front by multiphonon up-pumping and internal vibrational energy redistribution establishes a high-temperature, high-density transition state or series of transition states through which the chemical decomposition proceeds. The reaction rate constants for the initial unimolecular decomposition steps are accurately calculated using high-temperature, high-density transition-state theory. These early reactions are endothermic or weakly exothermic, but they channel most of the available energy into excited vibrational states of intermediate product species. The intermediate products transfer some of their vibrational energy back into the transition states, accelerating the overall reaction rates. As the decomposition progresses, the highly vibrationally excited diatomic and triatomic molecules formed in very exothermic chain reactions are rapidly vibrationally equilibrated by "supercollisions", which transfer large amounts of vibrational energy between these molecules. Along with vibrational -rotational and vibrational-translational energy transfer, these excited vibrational modes relax to thermal equilibrium by amplifying pressure wavelets of certain frequencies. These wavelets then propagate to the leading shock front and reinforce it. This is the physical mechanism by which the leading shock front is sustained by the chemical energy release.