Aquaculture is currently the fastest growing animal food production sector and will soon supply more than half of the world’s seafood for human consumption. Continued growth in aquaculture production is likely to come from intensification of fish, shellfish, and algae production. Intensification is often accompanied by a range of resource and environmental problems. We review several potential solutions to these problems, including novel culture systems, alternative feed strategies, and species choices. We examine the problems addressed; the stage of adoption; and the benefits, costs, and constraints of each solution. Policies that provide incentives for innovation and environmental improvement are also explored. We end the review by identifying easily adoptable solutions and promising technologies worth further investment.