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Global food demand is rising, and serious questions remain about whether supply can increase sustainably (FAO 2018). Land-based expansion is possible but may exacerbate climate change and biodiversity loss, and compromise the delivery of other ecosystem services (Olsen 2011; Foley et al. 2005, 2011; Mbow et al. 2019; Amundson et al. 2015). As food from the sea represents only 17% of the current production of edible meat, we ask how much food we can expect the ocean to sustainably produce by 2050. Here we examine the main food-producing sectors in the ocean—wild fisheries, finfish mariculture and bivalve mariculture—to estimate ‘sustainable supply curves’ that account for ecological, economic, regulatory and technological constraints. We overlay these supply curves with demand scenarios to estimate future seafood production. We find that under our estimated demand shifts and supply …