  In this work, we discuss the dense matter equation of state (EOS) for the
extreme range of conditions encountered in neutron stars and their mergers. The
calculation of the properties of such an EOS involves modeling different
degrees of freedom (such as nuclei, nucleons, hyperons, and quarks), taking
into account different symmetries, and including finite density and temperature
effects in a thermodynamically consistent manner. We begin by addressing
subnuclear matter consisting of nucleons and a small admixture of light nuclei
in the context of the excluded volume approach. We then turn our attention to
supranuclear homogeneous matter as described by the Chiral Mean Field (CMF)
formalism. Finally, we present results from realistic neutron-star-merger
simulations performed using the CMF model that predict signatures for
deconfinement to quark matter in gravitational wave signals.
