Neutron stars, whether isolated or in binary systems, are fantastic tools to explore fundamental aspects of gravitational and particle physics. After reviewing the mathematical and numerical tools that are needed to model neutron stars in their nonlinear dynamics, I will provide a few examples how neutron stars can be used to explore fundamental physics, ranging from their spectral properties, the possibility of phase transition to quark matter, the maximum mass, and up to the properties of the sound speed for matter at nuclear densities. Finally, I will report about a novel and tight correlation between the ratio of the energy and angular-momentum losses in the late-time portion of the post-merger signal, i.e., the "long ringdown", and the properties of the EOS at the highest pressures and densities in neutron-star cores.
