Detection of the gravitational waves emitted as a neutron star vibrates may enable us to answer questions about neutron star physics that it is impossible to answer with electromagnetic observations. Unfortunately, gravitational waves interact so weakly with matter that detection is a major challenge. In order to pick out a signal from the background noise, we must use cutting-edge data analysis techniques that rely on realistic models of the signal. To achieve this we must understand the source physics. Differential rotation, where different parts of a neutron star rotate with different angular velocities, can develop in several ways. These include the supernova in which the stars are born, non-linear effects associated with stellar vibrations, and rapid accretion. The collision of two neutron stars can also give rise to a long-lived differentially rotating remnant. Understanding the effects of differential rotation is critical, because it is after violent events like the supernova or a collision that we expect strong vibrations and gravitational wave emission. Differential rotation can dramatically alter the way in which a neutron star vibrates, introducing dynamical shear instabilities, and a continuous spectrum that is physically distinct from the discrete stable oscillation frequencies of a uniformly rotating star. I will discuss the type of vibrations that occur, their impact on the stability of the star, and the potential effects on gravitational wave emission.