Effective mitigation of climate change will require far-reaching transformations of electricity, heat, agricultural, transport, and other systems. The energy studies and modeling research that so often dominate academic and policy debates provide valuable insights into these transitions, but remain constrained by their focus on rational decision-making and their neglect of non-linear dynamics and broader social processes. This review describes insights from a complementary socio-technical approach that addresses the interdependent social, political, cultural, and technical processes of transitions. Focusing on the “multi-level perspective”, the paper conceptualizes transitions as arising from the alignment of processes within and between three analytical levels: niche innovations, socio-technical regimes, and the socio-technical landscape. This analytical framework is illustrated with a case study of the German electricity transition and is used to appraise low-carbon transitions in several other sectors. We end by articulating four lessons for managing low-carbon transitions.