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Because of the development of many-body theories of nuclear matter, the long-standing, open problem of the equation of state (EOS) of dense matter may be understood in the near future through the confrontation of theoretical calculations with laboratory measurements of nuclear properties \& reactions and increasingly accurate observations in astronomy. In this review, we focus on the following six aspects: 1) providing a survey of the quark mean-field (QMF) model, which consistently describes a nucleon and many-body nucleonic system from a quark potential; 2) applying QMF to both nuclear matter and neutron stars; 3) extending QMF formalism to the description of hypernuclei and hyperon matter, as well as hyperon stars; 4) exploring the hadron-quark phase transition and hybrid stars by combining the QMF model with the quark matter model characterized by the sound speed; 5) constraining interquark interactions through both the gravitational wave signals and electromagnetic signals of binary merger event GW170817; and 6) discussing further opportunities to study dense matter EOS from compact objects, such as neutron star cooling and pulsar glitches., Comment: 101 pages, 20 figures, invited review, to appear in Journal of High Energy Astrophysics

We study the effects of the symmetry energy on the neutron drip density and properties of nuclei in neutron star crusts. The nonuniform matter around the neutron drip point is calculated by using the Thomas--Fermi approximation with the relativistic mean-field model. The neutron drip density and the composition of the crust are found to be correlated with the symmetry energy and its slope. We compare the self-consistent Thomas--Fermi approximation with other treatments of surface and Coulomb energies and find that these finite-size effects play an essential role in determining the equilibrium state at low density., Comment: 33 pages, 14 figures, accepted for publication in Phys. Rev. C