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Climate change is resulting in rapid poleward shifts in the geographical distribution of many tropical fish species, but it is equally apparent that some fishes are failing to exhibit expected shifts in their geographical distribution. There is still little understanding of the species‐specific traits that may constrain or promote successful establishment of populations in temperate regions. We review the factors likely to affect population establishment, including larval supply, settlement and post‐settlement processes. In addition, we conduct meta‐analyses on existing and new data to examine relationships between species‐specific traits and vagrancy. We show that tropical vagrant species are more likely to originate from high‐latitude populations, while at the demographic level, tropical fish species with large body size, high swimming ability, large size at settlement and pelagic spawning behaviour are more likely to show …