Phototrophic marine organisms, particularly photosynthetic marine algae, are a diverse source of natural products ranging from lipid-based biofuels to pharmacologically-active compounds. The engineered production of both biomass and natural products is accomplished within enclosed, illuminated bioreactor systems called photobioreactors. This chapter describes the basic principles of photobioreactor analysis and design, and the biological factors that limit photobioreactor performance for the controlled cultivation of phototrophic marine organisms. There are three parts to this chapter. First, the quantitative growth characteristics of photosynthetic marine organisms in liquid cell suspension culture are described, including the use of photosynthetic biomass stoichiometry to describe nutrient incorporation into cellular biomass, and the combined effects of dissolved nutrient concentration and light intensity on cell growth rate. Second, the basic elements of photobioreactor design and operation are presented, focusing on models for predicting biomass production in batch or continuous cultivation modes within common photobioreactor configurations. Third, the limiting factors in photobioreactor design and operation are critically assessed from a quantitative point of view, focusing on light and carbon dioxide transfer limitations, and their effects on biomass production. Finally, future directions for the design and applications of enclosed photobioreactors are overviewed.