The ocean is a critical source of nutrition for billions of people, with potential to yield further food, profits, and employment in the future (1). But fisheries face a serious new challenge as climate change drives the ocean to conditions not experienced historically. Local, national, regional, and international fisheries are substantially underprepared for geographic shifts in marine animals driven by climate change over the coming decades. Fish and other animals have already shifted into new territory at a rate averaging 70 km per decade (2), and these shifts are expected to continue or accelerate (3). We show here that many species will likely shift across national and other political boundaries in the coming decades, creating the potential for conflict over newly shared resources.