While the economic debate on climate policy focuses on discounting, we do not know yet what to discount. The potential (non-discounted) socio-economic cost of climate change, indeed, is still unknown. Only a few studies have tried to estimate socio-economic costs of climate change. Most of them concluded that, for a warming of a few degrees, damages will be limited to a few percent of GDP. All these studies, however, have disregarded important mechanisms and have only considered the cost of a stabilized new climate. This article claims that the climate change issue should instead be framed in terms of the adaptation of socio-economic systems to a changing climate. Doing so, it calls for the taking into account of (1) the interaction between the uncertainty on future climate and the inertia of important economic sectors; (2) the short-term economic constraints that will be key in the response to climate shocks. Finally, the impacts of climate change cannot be estimated assuming that societies will always be able to manage in a perfect way the subsequent change in risks, as past experiences demonstrate our poor ability to do so. These mechanisms suggest that the uncertainty on future climate change damages is even larger than is usually acknowledged, and calls for additional research on climate change impacts.