Overexploitation of bycatch and target species in marine capture fisheries is the most widespread and direct driver of change and loss of global marine biodiversity. Bycatch in purse seine and pelagic longline tuna fisheries, the two primary gear types for catching tunas, is a primary mortality source of some populations of seabirds, sea turtles, marine mammals and sharks. Bycatch of juvenile tunas and unmarketable species and sizes of other fish in purse seine fisheries, and juvenile swordfish in longline fisheries, contributes to the overexploitation of some stocks, and is an allocation issue. There has been substantial progress in identifying gear technology solutions to seabird and sea turtle bycatch on longlines and to direct dolphin mortality in purse seines. Given sufficient investment, gear technology solutions are probably feasible for the remaining bycatch problems. More comprehensive consideration across species groups is needed to identify conflicts as well as mutual benefits from mitigation methods. Fishery-specific bycatch assessments are necessary to determine the efficacy, economic viability, practicality and safety of alternative mitigation methods. While support for gear technology research and development has generally been strong, political will to achieve broad uptake of best practices has been lacking. The five Regional Fisheries Management Organizations have achieved mixed progress mitigating bycatch. Large gaps remain in both knowledge of ecological risks and governance of bycatch. Most binding conservation and management measures fall short of gear technology best practice. A lack of performance standards, in combination with an inadequate observer coverage for all but large Pacific purse seiners, and incomplete data collection, hinders assessing measures’ efficacy. Compliance is probably low due to inadequate surveillance and enforcement. Illegal, unreported and unregulated tuna fishing hampers governance efforts. Replacing consensus-based decision-making and eliminating opt-out provisions would help. Instituting rights-based management measures could elicit improved bycatch mitigation practices. While gradual improvements in an international governance of bycatch can be expected, market-based mechanisms, including retailers and their suppliers working with fisheries to gradually improve practices and governance, promise to be expeditious and effective.