The combustion of energetic materials (explosives and propellants) exhibits some unique combustion behavior because of multiphase effects and because these materials can react rapidly to produce large amounts of gaseous products. Impact or thermal ignition of high explosives, (HE), results in deformation that can lead to fracture. Fracture, combined with high pressure dramatically increases the available surface area of HE materials where combustion can occur. Furthermore, the confining effect of small cracks can lead to localized elevated pressure and yield unusual combustion phenomena. Recent impact and thermal experiments on PBX 9501, HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) with a binder, have shown complex cracking patterns caused by impact or pressurization. Fast reactive waves have been observed to propagate through the cracks at about 500 m/s. These reactive waves are not typical deflagrations and are not detonations. In this presentation I will present various experimental observations that illustrate the various combustion problems of interest to those studying the combustion of energetic materials. This includes phenomena involved in ignition, normal deflagration, and the propagation of fast reactive waves in cracks. I will also give a brief description of the state of modeling efforts of these problems.