One contribution of 15 to a theme issue 'Innovation in animals and humans: understanding the origins and development of novel and creative behaviour'. Innovation and creativity are key defining features of human societies. As we face the global challenges of the twenty-first century, they are also facets upon which we must become increasingly reliant. But what makes Homo sapiens so innovative and where does our high innovation propensity come from? Comparative research on innovativeness in non-human animals allows us to peer back through evolutionary time and investigate the ecological factors that drove the evolution of innovativeness, whereas experimental research identifies and manipulates underpinning creative processes. In commenting on the present theme issue, I highlight the controversies that have typified this research field and show how a paradigmatic shift in our thinking about innovativeness will contribute to resolving these tensions. In the past decade, innovativeness has been considered by many as a trait, a direct product of cognition, and a direct target of selection. The evidence I review here suggests that innovativeness will be hereon viewed as one component, or even an emergent property of a larger array of traits, which have evolved to deal with environmental variation. I illustrate how research should capitalize on taxonomic diversity to unravel the full range of psychological processes that underpin innovativeness in non-human animals.