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This article reviews advances in modeling condensed-phase explosive detonation waves and their interaction with inerts for precision applications. We describe how constitutive data are obtained for a basic, predictive hydrodynamic model for explosives that subsequently can be studied numerically and analytically. Theory for multidimensional, time-dependent detonation dynamics is reviewed with a focus on freely propagating detonation and the asymptotic theory for quasi-one-dimensional, quasi-steady, detonation shock evolution (detonation shock dynamics). We discuss verification of these theories by direct numerical simulation (DNS) and validation by experiment. We describe a subscale model of detonation that uses an evolution equation to predict detonation dynamics and front states in complex engineering geometries that otherwise could not be computed by DNS. Four areas for future research are …