We are living in an age of uncertainty: the dynamics of modern societies and their impacts on the global environment—anthropogenic climate change in particular—have changed our relationship with the future and the conditions for planning it. Uncertainty has undermined traditional prognostics based on the future of the past, with “nature” as the static scenery, towards which the drama of history was unfolding. The history of scenario planning after World War II indicates that the age of uncertainty began some time around 1970. It is a symptom of the Great Acceleration. This context helps us see the broader picture behind the new challenges climate change poses to the insurance business in Europe and elsewhere. Expanding insurance globally has been recommended as a crucial strategy of climate change adaptation. However, the European case shows that climate change poses unprecedented adaptive challenges to the insurance business itself in a part of the world, where it has been well established for a long time. The frequency and severity of meteorological and climatological hazards are changing. Thus, the uncertainties of climate change create new uncertainties for insurance, as the example of crop insurance in Switzerland will illustrate.