  This is a review of theoretical results from the three-dimensional equations
of anisotropic elasticity or linear piezoelectricity on waves and vibrations in
quartz crystal plates. It covers both the classical results on acoustic wave
resonators and the relatively new applications in acoustic wave sensors. It
discusses the basic thickness modes with various complications due to
electrodes, mass loading, contact with fluids, and air gaps, etc. as well as
the more complicated transversely varying modes. These results are fundamental
for the understanding and design optimization of the widely used quartz crystal
plate resonators and sensors.
