After reviewing the physical properties of CO2 in seawater, including hydrate formation and decomposition, the solubility and biological pumps that drive the ocean carbon cycle are described. The various options to store CO2 in the ocean are then discussed; these include direct injection and dissolution, ocean bottom storage as liquid lakes or as gas hydrates, including the potential application of geomembranes, and biological sequestration options such as ocean fertilization (iron augmentation or deep water upwelling). The few in situ experiments that have been conducted are discussed. Ocean afforestation (macroalgal biomass cultivation for biofuel production) is also discussed as a means to increase CO2 uptake in the oceans.