  Neutron stars are the densest known objects in the universe and an ideal
laboratory for the strange physics of super-condensed matter. Theoretical
studies in connection with recent observational data of isolated neutron stars,
as well as binary neutron stars systems, offer an excellent opportunity to
provide robust solutions on the dense nuclear problem. In the present work, we
review recent studies concerning the applications of various theoretical
nuclear models on a few recent observations of binary neutron stars or
neutron-star--black-hole systems. In particular, using a simple and
well-established model, we parametrize the stiffness of the equation of state
with the help of the speed of sound. Moreover, in comparison to the recent
observations of two events by LIGO/VIRGO collaboration, GW170817 and GW190425,
we suggest possible robust constraints. We also concentrate our theoretical
study on the resent observation of a compact object with mass~$\sim
2.59_{-0.09}^{+0.08}~M_{\odot}$ (GW190814 event), as a component of a system
where the main companion was a black hole with mass $\sim 23~M_{\odot}$. There
is scientific debate concerning the identification of the low mass component,
as it falls into the neutron-star--black-hole mass gap. This is an important
issue since understanding the nature of GW190814 event will offer rich
information concerning the upper limit of the speed of sound in dense matter
and the possible phase transition into other degrees of freedom. We
systematically study the tidal deformability of a possible high-mass candidate
existing as an individual star or as a component in a binary neutron star
system. Finally, we provide some applications of equations of state of hot,
dense nuclear matter in hot neutron stars, protoneutron stars, and binary
neutron star merger remnants.
