Neutron stars are fascinating objects, the final stand of matter in the struggle to avoid becoming a black hole. The effort to understand them involves almost every subfield of physics you can think of, from general relativity via condensed matter physics to the world of subatomic particles.
In my talk I will try to explain some of the basic properties of neutron stars: The existence of a maximum and a minimum mass, and why the matter inside them can be treated as being at essentially zero temperature. This leads to the question of how neutron stars cool down, and I will close with a few words about how their thermal evolution can be used to learn about matter at high densities and, possibly, the properties of gravity.