This paper discusses a new approach to building mechanistic models for shock ignition and other reactive phenomena in heterogeneous solid explosives. In the proposed approach, hot spots are treated on a unifying framework (a hot-spot cell) to integrate the three, principal response behaviors of heterogeneous energetic materials: energy localization (hot-spot formation), temperature dependent chemical reactions, and heat flow. Hot spots are treated statistically through use of a size distribution and its evolution equation. Chemical reactions start at the surface of hot spots, and the products in turn become reactants for the subsequent bulk reactions. A heat conduction equation is solved for the temperature states in the hot-spot cell. Ignition and growth of the reactive burn depend on the complex interactions of the three processes: localized energy deposition, chemical reactions (surface as well as bulk), and heat flow. Coupling of the hot-spot model to hydrodynamic flow equations is based at present on a single cell, using mass averaged mixture equations of state and a common particle velocity for the constituents. The overall model is implemented on a two-dimensional Lagrangian code called CASH. To demonstrate the predictive capability of the model, we show several exploratory calculations using RDX as a model material. They include (1) shock ignition and growth-to-detonation, (2) quenching, and (3) curved detonation in a cylindrical specimen.