Neutron-star oscillations and instabilities play important roles in compact binary dynamics and provide insights into the physics of dense matter. In this talk, I will first discuss relativistic dynamical tides in neutron-star binaries, focusing on a framework based on the Mano–Suzuki–Takasugi solutions and its applications to tidal response and gravitational-wave signals. I will then turn to the oscillation spectra and hydrodynamical instabilities of rotating neutron stars, exploring how rotation modifies stellar oscillations and influences their dynamical stability. These studies provide a broader perspective on neutron-star dynamics and their implications for compact binary mergers.
