Neutron stars are fascinating objects requiring the understanding of many domains of physics ranging from condensed matter to nuclear physics and QCD. Matter is probed under extreme conditions of density, temperature, huge magnetic fields, ....

After reviewing recent observations and theoretical progress on various types of neutron stars, I will discuss some of the physics that may be important for their understanding, focusing on that closely related to nuclear physics such as the superfluid property and the nuclear excitations in the crust. Applications to the cooling of neutron stars will also be presented.