  In this article we discuss nonstationary models for inhomogeneous liquid
crystals driven out of equilibrium by flow. Emphasis is put on those models
which are used in the mathematics as well as in the physics literature, the
overall goal being to illustrate the mathematical progress on popular models
which physicists often just solve numerically. Our discussion includes the
Doi--Hess model for the orientational distribution function, the $Q$-tensor
model and the Ericksen--Leslie model which focuses on the director dynamics. We
survey particularly the mathematical issues (such as existence of solutions)
and linkages between these models. Moreover, we introduce the new concept of
relative energies measuring the distance between solutions of equation systems
with nonconvex energy functionals and discuss possible applications of this
concept for future studies.
