While innovation is expected to play a major role in decarbonization, the development and diffusion of low-carbon technologies are too slow in most sectors and countries to stabilize the climate. In this introductory paper to a Special Issue on “Innovation and climate change”, we review selected innovation studies literature, reflect on historical trends and insights, and cast light on future research on innovation and climate change. To set the stage for this Special Issue we present an analysis of key research topics, most influential papers and innovation journals, highlighting contributions across four interrelated themes: fostering climate action, shaping policy, promoting experimentation and learning, and examining effectiveness. While past studies and this special issue made significant contributions, we suggest that research on innovation have not sufficiently engaged with three important topics: i) blending behavioural change with technological innovation; ii) the socio-technical drivers of accelerated low-carbon transitions, and iii) the role of digital technologies as new venues of solutions to managerial challenges in addressing climate change. The nexus of climate change and innovation calls for different disciplines and coevolutionary views, as opposed to a traditional disciplinary focused approach. It also may require the need for broader, more inclusive and interdisciplinary research teams.