Understanding how breakthroughs emerge at the edges of possibility is fundamental to the study of innovation and progress. Such breakthroughs often appear as extreme events—rare, record-setting occurrences that push the boundaries of what a system can achieve. In this talk, I explore the connections between record statistics and models of innovation, drawing on urn models, statistical physics through sample space reducing processes, and evolutionary biology via Ewens' sampling formula. I then introduce a simple record statistics model with occasional resets, designed to capture the effects of innovation within competitive environments, such as evolution under selection or the progression of elite sports performance.