The development of quantum mechanics in the 1920s convinced physicists that future progress in understanding solids would flow from that discipline, and so continuum mechanics of solids was abandoned by physicists. Thus, success of the latter in late twentieth century is regarded as surprising by most.

We present an overview of the construction of a very general Lagrangian of a closed system of a dielectric crystal interacting with the electromagnetic field. The Lagrangian is first constructed for discrete particles, a long-wavelength (continuum) limit is taken in a manner to preserve all of the eigenmodes. The crystal can be of any class of symmetry, have any structural complexity, and have interactions between its various eigenmodes and between them and the electromagnetic field to any order of nonlinearity. All eigenmodes are included: electromagnetic, acoustic and optic modes of vibration, spin, and all polaritonic combinations of them.

The photoelastic effect was show to have been wrongly formulated for 155 years: the independent variable characterizing the deformation had been wrong! Thus, the interaction tensor has a more general symmetry. The accepted relation between the photoelastic effect and electrostriction was shown to have been wrong for almost as long. The elastic stiffness tensor was shown to lose its traditional symmetry when a soft optic mode became involved. All treatments of acoustic harmonic generation in piezoelectrics were shown to be wrong. The best derivation of optical activity was shown to have missed a fundamental contribution having a different dispersion. The Abraham - Minkowski controversy about the momentum of a light wave in a medium was resolved. The most general Poynting vector in a medium was found. Several nonlinear interactions were characterized and interpreted for the first time.