The marginal ice zones of the Arctic are regions of extreme importance to global biogeochemical cycles, in that they are sites of accumulation and transfer of organic matter within the food web and locations of significant fluxes of carbon, both inorganic and organic. Yet a complete seasonal description over the relevant time and space scales has not been conducted. Properly validated numerical models extend our ability to understand these oceanographic features because field studies are limited in their spatial and temporal coverage. Our knowledge of the mosaic of complex air-sea-ice interactions is good enough to relate the forces, through models, which control sea and ice motion, as well as the growth of phytoplankton. We review the use of models in investigations of marginal ice zones in the Arctic and conclude that the primary factor in regulating the initiation, development, and dissipation of ice edge phytoplankton blooms is vertical stratification. Furthermore, the spatial domain of the bloom is controlled by the ice dynamics and the response to local winds. Upwelling does occur at ice edges, but it is generally ineffective in directly stimulating phytoplankton growth. Any stimulation that does occur is via changes in the local ice cover (hence irradiance) field. Other mesoscale features such as eddies, fronts, or current meanders also influence the local biophysical interactions. The use of properly validated models in oceanographic research is a powerful tool for both posing and answering questions dealing with complex interactions that occur in the ocean.