  Recent equations of state for dense nuclear matter are discussed with
possible phase transitions arising in neutron stars such as pion, kaon and
hyperon kondensation, 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.
