  Recent developments in neutron star theory and observation are discussed.
Based on modern nucleon-nucleon potentials more reliable equations of state for
dense nuclear matter have been constructed. Furthermore, phase transitions such
as pion, kaon and hyperon condensation, superfluidity and quark matter can
occur in cores of neutron stars. Specifically, the nuclear to quark matter
phase transition and its mixed phases with intriguing structures is treated.
Rotating neutron stars with and without phase transitions are discussed and
compared to observed masses, radii and glitches. The observations of possible
heavy $\sim 2M_\odot$ neutron stars in X-ray binaries and QPO's require
relatively stiff equation of states and restrict strong phase transitions to
occur at very high nuclear densities only.
