We present the results of theoretical studies of the laser-induced damage in transparent solids containing absorbing inclusions. The investigation is based on the inclusion-initiated thermal explosion model. Key aspects of the model are considered: thermal instability initiated by the inclusions; a mechanism of photoionization of a surrounding layer of a host material by a thermal ultraviolet-radiation of laser-heated inclusions; the thermal instability kinetics, and an associated pulse-width dependence of the laser-induced damage threshold. Also, statistical features of the damage, caused by random spatial distribution of the inclusions in the materials, and a final stage of the damage process-a mechanical stress-produced crack formation-are analyzed. A comparison of the theoretical results, related to the pulse-width dependence of the damage threshold, with experimental data for some typical optical materials in a wide pulse-width range is presented.