Recent equations of state for dense nuclear matter are discussed with possi
ble phase transitions arising in neutron stars such as pion, kaon and hyper
on 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 wi
th and without phase transitions are given and compared to observed masses,
radii, temperatures and glitches. (C) 2000 Elsevier Science B.V. All right
s reserved.