Neutron stars are one of Nature's most intriguing stellar objects, containing matter under extraordinary conditions of density, temperature, and composition that are difficult to produce in the laboratory. In recent years, neutron star observations have begun to place novel constraints on the properties of strongly interacting matter in the high-density regime where current theoretical methods are challenged. At the same time, nuclear effective field theories have matured into a compelling framework to study nuclear matter with quantified uncertainties at moderate densities. In this talk, I will review recent advances in radio, x-ray, and gravitational-wave observations of neutron stars together with complementary developments from nuclear theory. The long-term goal is to understand the structure, phases, and dynamics of matter under extreme conditions and the implications for fundamental theories of the strong interaction.