Neutron stars are the remnant of massive stars and are created during the core-collapse supernova that marks the end of their life. With a radius of a tenth of kilometers for a mass of one to two times the one of the Sun, they are very dense and relativistic objects sustained by the strong interaction. This thesis deals with the theoretical modeling of three aspects of the evolution and dynamics of neutron stars : the thermal evolution of isolated neutron stars and neutron stars accreting matter from a companion star, the influence of the elastic properties of their solid parts on the rotation of isolated neutron stars and the rotational evolution of accreting neutron stars. The confrontation with the observations enables us to probe the properties of dense matter.
