Creativity and innovation are key elements in many different areas and disciplines since they represent the primary motor to explore new solutions in ever-changing and unpredictable environments. New biological traits and functions, new technological artefacts, new social, linguistic and cultural structures, new meanings, are very often triggered by the mutated external conditions. Unfortunately the detailed mechanisms through which humans, societies and nature express their creativity and innovate are largely unknown. The common intuition that one new thing often leads to another is captured, mathematically, by the notion of adjacent possible, introduced by Stuart Kauffman. Originally introduced in the framework of biology, the adjacent possible metaphor already expanded its scope to include all those things (ideas, linguistic structures, concepts, molecules, genomes, technological artefacts, etc.) that are one step away from what actually exists, and hence can arise from incremental modifications and recombination of existing material. In this talk I’ll present a mathematical framework, describing the expansion of the adjacent possible, whose predictions are borne out in several data sets drawn from social and technological systems. Finally I’ll discuss how games could represent a extraordinary framework to experimentally investigate basic mechanisms at play whenever we learn, create and innovate. I’ll present a few examples recently developed in the framework of the KREYON project (www.kreyon.net).