There are essentially four basic kinds of polarization mechanisms:
Interface polarization.
Surfaces, grain boundaries, interphase boundaries (including the surface of precipitates) may be charged, i.e. they contain dipoles which may become oriented to some degree in an external field and thus contribute to the polarization of the material.
Electronic polarization,
also called atom or atomic polarization. An electrical field will always displace the center of charge of the electrons with respect to the nucleus and thus induce a dipole moment as discussed before. Theparadigmatic materials for the simple case of atoms with a spherical symmetry are the noble gases in all aggregate forms.
Ionic polarization.
In this case a (solid) material must have some ionic character. It then automatically has internal dipoles, but these built-in dipoles exactly cancel each other and are unable to rotate. The external field then induces net dipoles by slightly displacing the ions from their rest position. The paradigmatic materials are all simple ionic crystals like NaCl.
Orientation polarization.
Here the (usually liquid or gaseous) material must have natural dipoles which can rotate freely. In thermal equilibrium, the dipoles will be randomly oriented and thus carry no net polarization. The external field aligns these dipoles to some extent and thus induces a polarization of the material. The paradigmatic material is water, i.e. H2O in its liquid form.
Some or all of these mechanisms may act simultaneously. Atomic polarization, e.g., is always present in any material and thus becomes superimposed on whatever other mechanism there might be.
Real materials thus can be very complicated in their dielectric behavior. In particular, non-spherical atoms