Hybrid zones are 'natural laboratories' for studying the origin, maintenance and demise of species. Theory predicts that hybrid zones can move in space and time, with significant consequences for both evolutionary and conservation biology, though such movement is often perceived as rare. Here, a review of empirical studies of moving hybrid zones in animals and plants shows 23 examples with observational evidence for movement, and a further 16 where patterns of introgression in molecular markers could be interpreted as signatures of movement. The strengths and weaknesses of methods used for detecting hybrid zone movement are discussed, including long-term replicated sampling, historical surveys, museum/herbarium collections, patterns of relictual populations and introgression of genetic markers into an advancing taxon. Factors governing hybrid zone movement are assessed in the light of the empirical studies, including environmental selection, competition, asymmetric hybridization, dominance drive, hybrid fitness, human activity and climate change. Hybrid zone movement means that untested assumptions of stability in evolutionary studies on hybrid zone can lead to mistaken conclusions. Movement also means that conservation effort aimed at protecting against introgression could unwittingly favour an invading taxon. Moving hybrid zones are of wide interest as examples of evolution in action and possible indicators of environmental change. More long-term experimental studies are needed that incorporate reciprocal transplants, hybridization experiments and surveys of molecular markers and population densities on a range of scales.