Effective mitigation of climate change will require far-reaching transformations of electricity, heat, agricultural, transport and other systems. The energy studies and modelling research that so often dominates 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 paper 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’ (MLP), 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 used to appraise low-carbon transitions in several other sectors. We end by articulating four lessons for managing low-carbon transitions.