  The properties of dense QCD matter are delineated through the construction of
equations of state which should be consistent with QCD calculations in the low
and high density limits, nuclear laboratory experiments, and the neutron star
observations. These constraints, together with the causality condition of the
sound velocity, are used to develop the picture of hadron-quark continuity in
which hadronic matter continuously transforms into quark matter (modulo small
1st order phase transitions). For hadronic matter (at baryon density nB > ~2n0
with n0 ~ 0.16 fm^(-3) being the nuclear saturation density) we use equations
of state by Togashi et al. based on microscopic variational many-body
calculations, and for quark matter (nB > ~5n0) we construct equations of state
using a schematic quark model (with strangeness) whose interactions are
motivated by the hadron phenomenology. The region between hadronic and quark
matters (~2n0 < nB < ~5n0), which is most difficult to calculate, is treated by
highly constrained interpolation between nuclear and quark matter equations of
state. The resultant unified equation of state at zero temperature and
beta-equilibrium, which we call Quark-Hadron-Crossover (QHC18 and QHC19), is
consistent with the measured properties of neutron stars and in addition gives
us microscopic insights into the properties of dense QCD matter. In particular
to ~10n0 the gluons can remain as non-perturbative as in vacuum and the
strangeness can be as abundant as up- and down-quarks at the core of two-solar
mass neutron stars. Within our modeling the maximum mass is found less than
~2.35 times solar mass and the baryon density at the core ranges in ~5-8n0.
