It is becoming increasingly clear that deep and rapid transitions in technologies, infrastructures and ways of organising the economy are imperative if we are to live safely within planetary boundaries. But what historical precedents are there for such profound shifts within short spaces of time, and what were the enabling conditions? When have transitions in sectors such as energy, food, finance and transport come about before, and how would they be brought about again? Do these episodes shed any analogous light on our current collective predicament? This paper develops an account of the politics and prospects of deeper transitions towards sustainability based on a critical empirical, but theoretically informed, reading of previous socio-technical transitions. The scale and urgency of our current ecological predicament is daunting and can be disempowering in the absence of strategic thinking about when analogous challenges have been encountered before and how societies have sought to overcome them. Providing a combination of concrete empirical examples drawn both from academic literature and a series of public workshops reflecting on these themes, this paper seeks to provide a basis for understanding as well as engaging with the scope for accelerated transitions within and beyond capitalism.