Phononic crystals are structures with spatially periodic variations in density and sound velocities. The most fascinating feature of phononic crystals is the existence of stop bands or band gaps in their dispersion relation, where no phonons are allowed to propagate. As a result, phononic crystals have great promise for achieving precise control over propagation of sound and other mechanical waves. In this talk our recent investigation of 2‐D and 3‐D hypersonic phononic crystals with band gaps in GHz frequency range will be presented and their potential applications as acoustic mirrors, lenses, waveguides, etc. will be discussed. High‐quality single‐crystalline structures were fabricated using interference lithography. Their phonon dispersion relation was directly measured with Brillouin light scattering. Finite‐element analysis was employed to compute theoretical dispersion relation and provide interpretation for the experimentally observed propagation modes [T. Gorishnyy etal., Phys. Rev. Let. 94, 115501 (2005); T. Gorishnyy etal., Physics World 18 (12), 24–29 (2005)]. [Work supported by NSF Grants DMR‐0308133 and DMR‐0414974.]