I will discuss efforts to interpret recent gravitational wave and x-ray 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. 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 conclude by highlighting the need for next-generation gravitational wave observatories such as Cosmic Explorer and Einstein Telescope and outline their discovery potential.