Background: Climate change impacts are felt disproportionately in developing countries, and in particular Southern Asia experiences the most damaging hydrometeorological events in the world, with loss of life from past cyclones in the hundreds of thousands. Despite this, the Bay of Bengal cyclone basin receives far less research attention than many of the others around the world. Here, we study the historical and future impacts of Super Cyclone Amphan, which made landfall in May 2020, bringing storm surges of 2-4 meters to coastlines of India and Bangladesh. Methods: In this modelling study, we combine projections of sea level rise from the Coupled Model Intercomparison Projection, phase 6 (CMIP6), with estimates of storm surge using a dynamic storm surge model. Sampling the spectrum of possible sea level rises, we consider a low, medium and high scenario, based on projections in 2100. We then feed these into a flood inundation model to simulate storm surge-induced flooding, had Cyclone Amphan occurred in these future worlds. Finally, we consider the change in future population growth and urbanisation, thereby calculating the change in population exposure to these future flooding events. Our approach is that of the extreme event attribution community, but projecting into the future rather than interrogating the past. Findings: We find that in 2100, the local sea level rise in the Bay of Bengal during the pre-monsoon cyclone season is between 0.32-0.84 m, depending on which emissions scenario is followed. If a Cyclone Amphan-scale storm surge occurred on top of that sea level rise, the future population of both India and Bangladesh will be more exposed, with India showing >200% increased exposure to extreme (>3 m) and moderate (>1 m) flooding under a high emissions scenario, and Bangladesh showing ~60-80% increased exposure to the same scenarios. The majority of this change in both countries comes from sea level rise rather than population changes, and in Bangladesh the future population change contributes negatively to the change in exposure, as more citizens migrate further inshore. However, if we follow an emissions scenario consistent with meeting the upper Paris Agreement climate goal, we project very little change in exposure. Interpretation: There is an urgent need to reduce carbon emissions to net zero, to prevent the negative impacts of climate change. By far the majority of cyclone research has been undertaken for countries such as America and Japan, with less resilient countries such as those in South Asia, which are more sensitive to changes in climate, seeing far less attention. With Cyclone Amphan occurring at the height of the COVID-19 crisis, we highlight how the risk was compounded and recommend that future climate risk assessments explicitly account for these potential non-linearities. Funding Statement: The main funding is from the Natural Environment Research Council.Declaration of Interests: The authors declare no competing interests.