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This paper reviews the basic properties of shear-horizontal (SH)-type surface acoustic waves (SAWs) and bulk acoustic waves (BAWs). As one of the simplest cases, the structure supporting Bleustein-Gulyaev-Shimizu waves is considered, and their excitation and propagation are discussed from various view points. First, the formalism based on the complex integral theory is presented, where the surface is assumed to be covered with an infinitesimally thin metallic film, and it is shown how the excitation and propagation of SH-type waves are affected by the surface perturbation. Then, the analysis is extended to a periodic grating structure, and the behavior of SH-type SAWs under the grating structure is discussed. Finally, the origin of the leaky nature is explained.