  We give a brief review of some generalized continuum theories applied to the
crystals with complicated microscopic structure. Three different ways of
generalization of the classical elasticity theory are discussed. One is the
high-gradient theory, another is the micropolar type theory and the third one
is the many-field theory. The importance of the first two types of theories has
already been established, while the theory of the third type still has to be
developed. With the use of 1D and 2D examples we show for each of these
theories where they can be and should be applied, separately or in a
combination.
