Technological innovations seem to be among the great promises for achieving the urgent modernisation of economies towards carbon-neutrality. Ranging from fusion energy, bio-based fuels, carbon capture and storage to PV panels and so-called smart energy systems, plenty of technologies promise to reduce use or greenhouse gas emissions of carbon based energy sources. This techno-centric view disregards to a great extent that technological change affects and is affected by societal practices and norms. The present paper argues that contemporary methodological approaches informed by complex systems and social practices theories provide urgently needed insights into innovation for decarbonisation. It specifically addresses the following questions: Why are current conceptualisations of innovation narrowly framed and with what consequences? How would a framing of innovation grounded on complex systems and social practice theories improve the understanding of opportunities and challenges at stake with innovation for decarbonisation? How could this framing help uncover and deploy an important and still often neglected social innovation potential? In a nutshell, the authors advocate for research and policy agendas that are firmly grounded in social practices and take complex and dynamic interactions of energy supply and demand as departing point to seriously reflect about the transitions that are put before us.