The flow field developed behind shock waves in a pure gaseous medium is well known and documented in all gasdynamics textbooks. This is not the case when the gaseous medium is seeded with small solid particles. The present review treats various cases of shock waves propagation into a gas-dust suspension (dusty shock waves). It starts (chapter 1) with basic definitions of two-phase (gas-dust) suspensions and presents a general form of the conservation equations which govern dusty shock wave flows. In chapter two, the simple case of a steady flow of a suspension consisting of an inert dust and a perfect gas through a normal shock wave is studied. The effect of the dust presence, and of changes in its physical parameters, on the post-shock wave flow are discussed. Obviously, these discussions are limited to relatively weak shock waves (perfect gas). For stronger normal shock waves, the assumption of a perfect gas no longer holds. Therefore, in chapter three, real gas effects (ionization or dissociation) are taken into account when calculating the post-shock flow field. In chapter four, the dust chemistry is included and its effects on the post-shock flow is studied. In order to emphasize the role played by the dust chemistry, a comparison between a reactive and a similar inert suspension is presented. The case of an oblique shock wave in a dusty gas is discussed in chapter five. In all cases treated in chapters two to five the flow is steady; however, in many engineering applications this is not the case. In reality, even for the simplest case of a one-dimensional flow (normal shock wave propagation into quiescent suspension—the dusty shock tube) the shock wave attenuates and the flow field behind it is not steady. This case is treated in chapter six. The cases treated in chapters two to six deal with planar shock waves. However, all explosion generated shock waves in the atmosphere are spherical. Due to the engineering importance of this case, the post-shock flow for spherical shock waves in a dusty gas is studied, in detail, in chapter seven. It is shown in the present review that the dust presence has significant effects on the post-shock flow field. In all cases studied, a relaxation zone is developed behind the shock wave front. Throughout this zone momentum and energy exchange between the two phases of the suspension takes place. Through these interactions a new state of equilibrium is reached. The extent of the relaxation zone depends upon the dust loading ratio, the dust particle diameter, its specific heat capacity, and the dust spatial density. Due to the complexity of conducting experimental investigations with dusty shock waves, the number of published experimental results is very limited. As a result most of the present review contains numerical studies. However, in the few cases where experimental data are available, (e.g. dusty shock tube flow; see chapter six) a comparison between the numerical and experimental results is given.