Recent advances in the theory and application of dynamic magnetoelastic coupling in single-crystal ferromagnets and antiferromagnets are reviewed. As background, a linear model of a magnetoelastic ferromagnet is constructed by demanding that the small-signal equations lead to small-signal power-energy and stress-momentum conservation. Self-consistent boundary conditions are also discussed. Magnetoelastic excitations are reviewed both as waves and quasiparticles and coupled-mode analysis is used to describe the propagation of spin-elastic waves in a crystal subjected to time-varying and/or space-varying magnetic bias fields. In such cases, the character of a wave packet can change. This is especially true for longitudinal-elastic/spin waves propagating in yttrium iron garnet (YIG). Microwave and optical experiments dealing with this important case are recounted; the latter demonstrates that strong Bragg scattering of coherent 1150-nm wavelength laser radiation can be used to allow one to "see" the microwave (1.5 GHz) spin/elastic conversion in detail.