Many studies have concluded that the current global economy can transition from fossil fuels to be powered entirely by renewable energy. While supporting such transition, we critique analysis purporting to conclusively demonstrate feasibility. Deep uncertainties remain about whether renewables can maintain, let alone grow, the range and scale of energy services presently provided by fossil fuels. The more optimistic renewable energy studies rely upon assumptions that may be theoretically or technically plausible, but which remain highly uncertain when real-world practicalities are accounted for. This places investigation of energy-society futures squarely in the domain of post-normal science, implying the need for greater ‘knowledge humility’ when framing and interpreting the findings from quantitative modelling exercises conducted to investigate energy futures. Greater appreciation for the limits of what we can know via such techniques reveals ‘energy descent’ as a plausible post-carbon scenario. Given the fundamental dependence of all economic activity on availability of energy in appropriate forms at sufficient rates, profound changes to dominant modes of production and consumption may be required, a view marginalised when more techno-optimistic futures are assumed. Viewing this situation through the lens of ‘post-normal times’ opens avenues for response that can better support societies in navigating viable futures.