Fishing in the open ocean often results in unwanted effects on target species, and interactions with non-target species (direct interactions) or influences on the prey or habitat of target and non-target species (indirect interactions). A number of conflicts and trade-offs exist in the harvesting of pelagic species, including (i) maximizing future food production given the depleted state of some stocks; (ii) minimizing bycatch of non-target species, (iii) setting ecosystem allocation rules for non-target top predators, such as seabirds, and (iv) maximizing value and livelihoods for local economies. Climate change can be expected to exacerbate some of these conflicts as the ranges of species and their habitats change over varying geographic, depth and temporal scales. Understanding the distribution of these impacts can be difficult due to the scarcity of observational data on species and ecosystems. Resolving all these conflicts is achievable with current approaches and technologies. Nevertheless, managing fishery production systems to provide fish for food security and conserving biodiversity will be particularly challenging. The complexity added by climate change can be managed with greater use of early warning systems and precautionary management.