Comparing measurements of redshift-space distortions (RSDs) with geometrical observations of the expansion of the Universe offers tremendous potential for testing general relativity on very large scales. The basic linear theory of RSDs in the distant-observer limit has been known for 25 years and the effect has been conclusively observed in numerous galaxy surveys. The next generation of galaxy survey will observe many millions of galaxies over volumes of many tens of Gpc 3 . They will provide RSD measurements of such exquisite precision that we will have to carefully analyse and correct for many systematic deviations from this simple picture in order to fully exploit the statistical precision obtained. We review RSD theory and show how ubiquitous RSDs actually are, and then consider a number of potential systematic effects, shamelessly highlighting recent work in which we have been involved. This review ends by looking ahead to the future surveys that will make the next generation of RSD measurements.