  The microscopic composition and properties of matter at super-saturation
densities have been the subject of intense investigation for decades. The
scarcity of experimental and observational data has lead to the necessary
reliance on theoretical models. However, there remains great uncertainty in
these models, which, of necessity, have to go beyond the over-simple assumption
that high density matter consists only of nucleons and leptons. Heavy strange
baryons, mesons and quark matter in different forms and phases have to be
included to fulfil basic requirements of fundamental laws of physics. In this
review the latest developments in construction of the Equation of State (EoS)
of high-density matter at zero and finite temperature assuming different
composition of the matter are surveyed. Critical comparison of model EoS with
available observational data on neutron stars, including gravitational masses,
radii and cooling patterns is presented. The effect of changing rotational
frequency on the composition of neutron stars during their lifetime is
demonstrated. Compatibility of EoS of high-density, low temperature compact
objects and low density, high temperature matter created in heavy-ion
collisions is discussed.
