  Spinning neutron stars, when observed as pulsars, are seen to undergo
occasional spin-up events known as glitches. Despite several decades of study,
the physical mechanisms responsible for glitches are still not well understood,
but probably involve an interplay between the star's outer elastic crust, and
the superfluid and superconducting core that lies within. Glitches will be
accompanied by some level of gravitational wave emission. In this article we
review proposed models that link gravitational wave emission to glitches,
exploring both short duration burst-like emission, and longer-lived signals. We
illustrate how detections (and in some cases, non-detections) of gravitational
signals probe both the glitch mechanism, and, by extension, the behaviour of
matter at high densities.
