Innovation or the creation and diffusion of new material, social and cultural things in society has been widely studied in sociology and across the social sciences, with investigations sufficiently diverse and dispersed to make them unnavigable. This complexity results from innovation's importance for society, but also the fundamental paradox underlying innovation science: When innovation becomes predictable, it ceases to be an engine of novelty and change. Here we review innovation studies and show that innovations emerge from contexts of discord and disorder, breaches in the structure of prior success, through a process we term destructive creation. This often leads to a complementary process of creative destruction whereby local structures protect and channel the diffusion of successful innovations, rendering alternatives obsolete. We find that social scientists naturally focus far more on how social and cultural contexts influence material innovations than the converse. We highlight computational tools that open new possibilities for the analysis of novel content and context in interaction, and show how this brings us empirically toward the broader range of possibilities that complex systems and science studies have theorized—and science fiction has imagined—the social, cultural and material structures of innovation conditioning each other's change through cycles of disruption and development.

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