Neutron stars provide us with the largest samples of degenerate matter in the Universe. Because of the high density of matter in them, understanding these stars requires input from numerous subfields of physics and I shall begin by showing how their properties may be estimated from elementary physical arguments. Subsequently, I shall describe how the observation within the past five years of neutron stars weighing twice as much as our Sun has made it possible to pin down much better the properties of matter at supranuclear densities.