Wojtak, Hansen and Hjorth and others have measured the long-predicted gravitational redshift of light escaping from galaxy clusters. The effect is very small, corresponding to a velocity shift of only ~10 km/s, but the result appears to be fairly robust and seemed to be in good agreement with general relativity predictions and possibly in conflict with some alternative theories. The effect was initially imagined to be a simple astronomical analogue of the famous terrestrial Pound and Rebka experiment that verified Einstein's theoretical prediction. However, it was soon realised that the physics of this effect is considerably more complex. As I shall describe, there are actually three other contributions to the measured signal that need to be taken into account. I shall describe recent attempts to model these effects using N-body experiments, and how this effect may be useful for testing alternative theories of gravity. Understanding this apparently simple effect reveals some subtleties in special relativity and also sheds light on the interpretation of redshifts in cosmology.