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Ocean metabolism constitutes a complex, multiscale ensemble of biochemical reaction networks harbored within and between the boundaries of a myriad of organisms. Gaining a quantitative understanding of how these networks operate requires mathematical tools capable of solving in silico the resource allocation problem each cell faces in real life. Toward this goal, stoichiometric modeling of metabolism, such as flux balance analysis, has emerged as a powerful computational tool for unraveling the intricacies of metabolic processes in microbes, microbial communities, and multicellular organisms. Here, we provide an overview of this approach and its applications, future prospects, and practical considerations in the context of marine sciences. We explore how flux balance analysis has been employed to study marine organisms, help elucidate nutrient cycling, and predict metabolic capabilities within diverse marine environments, and highlight future prospects for this field in advancing our knowledge of marine ecosystems and their sustainability.