this book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. the first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. acceleration waves and shock waves are the focus in the next two chapters. numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. the final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest. this book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.