Phases of dense matter in neutron stars

Recent equations of state for dense nuclear matter are discussed with possible phase transitions arising in neutron stars such as pion, kaon and hyperon condensation, superfluidity and quark matter. Specifically, we treat the nuclear to quark matter phase transition, the possible mixed phase and its structure. A number of numerical calculations of rotating neutron stars with and without phase transitions are given and compared to observed masses, radii, temperatures and glitches.