Neutron stars are fascinating laboratories of extreme physics. Any realistic dynamical model must be able to simultaneously handle solids, superfluids and superconductors. Some neutron stars also possess huge magnetic fields that may play an important role. In order to take full advantage of existing and future observations the models should be built within General Relativity.
I will give a brief introduction to a theory of continuum mechanics of systems with multiple constituents suitable to describe neutron stars. I will then give examples of how we may use our models to explain observations and extract information about the properties of dense matter.