Innovations are generally unexpected, often spectacular changes in phenotypes and ecological functions. The contributions to this theme issue are the latest conceptual, theoretical and experimental developments, addressing how ecology, environment, ontogeny and evolution are central to understanding the complexity of the processes underlying innovations. Here, we set the stage by introducing and defining key terms relating to innovation and discuss their relevance to biological, cultural and technological change. Discovering how the generation and transmission of novel biological information, environmental interactions and selective evolutionary processes contribute to innovation as an ecosystem will shed light on how the dominant features across life come to be, generalize to social, cultural and technological evolution, and have applications in the health sciences and sustainability. This article is part of the theme issue ‘Process and pattern in innovations from cells to societies’.