I will discuss efforts to interpret recent multi-messenger observations of neutron stars using advances in theory and modeling. These studies have provided new insights into the sound speed in dense matter and low-temperature properties, such as its specific heat and transport phenomena. Neutron stars can also be excellent sites to look for dark matter. I will briefly discuss harnessing neutron star observations to constrain or discover dark matter candidates with sub-GeV masses. I will comment on how next-generation gravitational wave observatories such as Cosmic Explorer and Einstein Telescope can revolutionize the field and outline their discovery potential.