There is a need to better understand the survivorship of discarded fishes, both for commercial stocks and species of conservation concern. Within European waters, the landing obligations that are currently being phased in as part of the European Union's reformed common fisheries policy means that an increasing number of fish stocks, with certain exceptions, should not be discarded unless it can be demonstrated that there is a high probability of survival. This study reviews the various approaches that have been used to examine the discard survival of elasmobranchs, both in terms of at-vessel mortality (AVM) and post-release mortality (PRM), with relevant findings summarized for both the main types of fishing gear used and by taxonomic group. Discard survival varies with a range of biological attributes (species, size, sex and mode of gill ventilation) as well as the range of factors associated with capture (e.g. gear type, soak time, catch mass and composition, handling practices and the degree of exposure to air and any associated change in ambient temperature). In general, demersal species with buccal-pump ventilation have a higher survival than obligate ram ventilators. Several studies have indicated that females may have a higher survival than males. Certain taxa (including hammerhead sharks Sphyrna spp. and thresher sharks Alopias spp.) may be particularly prone to higher rates of mortality when caught.