The impact of fishing on chondrichthyan stocks around the world is currently the focus of considerable international concern. Most chondrichthyan populations are of low productivity relative to teleost fishes, a consequence of their different life-history strategies. This is reflected in the poor record of sustainability of target shark fisheries. Most sharks and some batoids are predators at, or near, the top of marine food webs. The effects of fishing are examined at the single-species level and through trophic interactions. We summarize the status of chondrichthyan fisheries from around the world. Some 50% of the estimated global catch of chondrichthyans is taken as by-catch, does not appear in official fishery statistics, and is almost totally unmanaged. When taken as by-catch, they are often subjected to high fishing mortality directed at teleost target species. Consequently, some skates, sawfish, and deep-water dogfish have been virtually extirpated from large regions. Some chondrichthyans are more resilient to fishing and we examine predictions on the vulnerability of different species based on their life-history and population parameters. At the species level, fishing may alter size structure and population parameters in response to changes in species abundance. We review the evidence for such density-dependent change. Fishing can affect trophic interactions and we examine cases of apparent species replacement and shifts in community composition. Sharks and rays learn to associate trawlers with food and feeding on discards may increase their populations. Using ECOSIM, we make some predictions about the long-term response of ecosystems to fishing on sharks. Three different environments are analysed: a tropical shelf ecosystem in Venezuela, a Hawaiian coral reef ecosystem, and a North Pacific oceanic ecosystem.