This paper presents the concept of raising seaweeds and other valuable organisms with the aid of huge structures ('ocean farms') emplaced in the surface waters of the open oceans. Potential advantages from and difficulties to be expected in realizing the associated technologies are briefly set forth. Much of the published literature pertaining to the concept is referenced and summarized. Wave-powered upwelling of cool, nutrient-rich waters through vertical pipes extending to depths of 100-300 m is indicated as desirable. Technologies are outlined for using the harvested seaweeds to create foods and other valuable products such as animal feeds, fertilizers, fibers, plastics, synthetic natural gas (methane), and alcohol and gasoline fuels. Results from site selection studies and economic analyses are given. It appears that dynamically positioned farms orbiting with the surface current patterns typically found on the ocean will be most cost-effective. The general conclusion is stated that open ocean farming will become economically more feasible as the cheaper fossil fuels and food producing lands of the earth become increasingly consumed in the course of the next century.