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.
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