The major goal of this PhD project is to investigate the fundamental properties of energetic materials, including their atomic and electronic structures, as well as mechanical properties, and relate these to the fundamental mechanisms of shock wave and detonation propagation using state-of-the-art simulation methods. The first part of this PhD project was aimed at the investigation of static properties of energetic materials (EMs) with specific focus on 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). The major goal was to calculate the isotropic and anisotropic equations of state for TATB within a range of compressions not accessible to experiment, and to make predictions of anisotropic sensitivity along various crystallographic directions. The second part of this PhD project was devoted to applications of a novel atomic-scale simulation method, referred to as the moving window molecular dynamics (MW-MD) technique, to study the fundamental mechanisms of condensed-phase detonation. Because shock wave is a leading part of the detonation wave, MW-MD was applied to demonstrate its effectiveness in resolving fast non-equilibrium processes taking place behind the shock-wave front during shock-induced solid-liquid phase transitions in crystalline aluminum. Next, MW-MD was used to investigate the fundamental mechanisms of detonation propagation in condensed energetic materials. Due to the chemical complexity of real EMs, a simplified AB model of a prototypical energetic material was used. The AB interatomic potential, which describes chemical bonds, as well as chemical reactions between atoms A and B in an AB solid, was modified to investigate the mechanism of the detonation wave propagation with different reactive activation barriers. The speed of the shock or detonation wave, which is an input parameter of MW-MD, was determined by locating the Chapman-Jouguet point along the reactive Hugoniot, which was simulated using the constant number of particles, volume, and temperature (NVT) ensemble in MD. Finally, the detonation wave structure was investigated as a function of activation barrier for the chemical reaction AB+B ⇒ A+BB. Different regimes of detonation propagation including 1-D laminar, 2-D cellular, and 3-D spinning and turbulent detonation regimes were identified.