Anthropogenic greenhouse gas emissions cause multiple changes in the ocean and its ecosystems through climate change and ocean acidification. These changes can occur progressively with rising atmospheric carbon dioxide concentrations, but there is also the possibility of large-scale abrupt, and/or potentially irreversible changes, which would leave limited opportunity for marine ecosystems to adapt. Such changes, either progressive or abrupt, pose a threat to biodiversity, food security, and human societies. However, it remains notoriously difficult to determine exact limits of a “safe operating space” for humanity. Here, we map, for a variety of ocean impact metrics, the crossing of limits, which we define using the available literature and to represent a wide range of deviations from the unperturbed state. We assess the crossing of these limits in three future emission pathways: two climate mitigation scenarios, including an overshoot scenario, and one high-emission no-mitigation scenario. These scenarios are simulated by the latest generation of Earth system models and large perturbed-parameter ensembles with two Earth system models of intermediate complexity. Using this comprehensive model database, we estimate the timing and warming level at which 15 different impact metrics exceed 4 limits, along with an assessment of the associated uncertainties. We find that under the high-emissions scenario, the strongest severity of impacts is expected with high probability for marine heatwaves’ duration, loss of Arctic summer sea ice extent, expansion of ocean areas that are undersaturated with respect to aragonite, and decrease in plankton biomass. The probability of exceeding a given limit generally decreases clearly under low-emissions scenario. Yet, exceedance of ambitious limits related to steric sea level rise, Arctic summer sea ice extent, Arctic aragonite undersaturation, and plankton biomass are projected to be difficult to avoid (high probability) even under the low-emissions scenario. Compared to the high-emissions scenario, the scenario including a temporary overshoot reduces with high probability the risk of exceeding limits by year 2100 related to marine heatwave duration, Arctic summer sea ice extent, strength of the Atlantic meridional overturning circulation, aragonite undersaturation, global deoxygenation, plankton biomass, and metabolic index. Our study highlights the urgent need for ambitious mitigation efforts to drastically minimize extensive impacts and potentially irreversible changes to the world’s ocean ecosystems.