There are three main polarisation mechanisms that can occur within a dielectric material: electronic polarisation, ionic polarisation (sometimes referred to as atomic polarisation) and orientational polarisation. The animation below illustrates how each of these mechanisms functions on the microscopic scale.
All non-conducting materials are capable of electronic polarisation, which is why all insulators are dielectric to some degree. In contrast, the ionic and orientational modes are only available to materials possessing ions and permanent dipoles respectively.
Another contribution to polarization is space charge, or the accumulation of mobile charges at structural surfaces and interfaces. Rather than being a direct property of a material this is only a feature of heterostructures, and hence is not discussed further here.