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 (2n_0 < 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 give 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 exist at the core of neutron stars with 2-solar mass.