Neutron stars are excellent emitters of gravitational waves. Squeezing matter beyond nuclear densities invites exotic physical processes, many of which violently transfer large amounts of mass at relativistic velocities, disrupting spacetime and generating copious quantities of gravitational radiation. I review mechanisms for generating gravitational waves with neutron stars. This includes gravitational waves from radio and millisecond pulsars, magnetars, accreting systems, and newly born neutron stars, with mechanisms including magnetic and thermoelastic deformations, various stellar oscillation modes, and core superfluid turbulence. I also focus on what physics can be learnt from a gravitational wave detection, and where additional research is required to fully understand the dominant physical processes at play.
