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Marine phytoplankton have many obvious characters, such as rapid cell division rates and large population sizes, that give them the capacity to evolve in response to global change on timescales of weeks, months or decades. However, few studies directly investigate if this adaptive potential is likely to be realized. Because of this, evidence of to whether and how marine phytoplankton may evolve in response to global change is sparse. Here, we review studies that help predict evolutionary responses to global change in marine phytoplankton. We find limited support from experimental evolution that some taxa of marine phytoplankton may adapt to ocean acidification, and strong indications from studies of variation and structure in natural populations that selection on standing genetic variation is likely. Furthermore, we highlight the large body of literature on plastic responses to ocean acidification available, and evolutionary theory that may be used to link plastic and evolutionary responses. Because of the taxonomic breadth spanned by marine phytoplankton, and the diversity of roles they fill in ocean ecosystems and biogeochemical cycles, we stress the necessity of treating taxa or functional groups individually.