This book deals with some of the problems of nonlinear shock structures. A rigorous theoretical investigation has been made on nonlinear propagation of the dust-electron-acoustic (DEA) and dust-acoustic (DA) shock waves in both weakly and strongly coupled dusty plasmas. The basic features of the small but finite amplitude DEA and DA shock waves have been theoretically investigated by using the reductive perturbation technique. The effects of non-planner geometry, polarization force and fast (nonthermal) paticles on DA shock waves have also been thoroughly investigated. It has been shown that these effects not only significantly modify the basic features of the DEA and DA shock waves, but also introduce some important new features. The basic features and the physics insight of the DEA and DA shock waves, which are relevant to space environments (e. g. upper part of the ionosphere) and laboratory devices (viz. rf and dc discharges), have been pin-pointed and discussed.