As innovation entails risk, it seems only natural that risk management practises should be the core enablers of innovation within companies. Yet, the risk management function is often portrayed as the innovation “killer" in organisations. In this chapter we shed light onto this innovation and risk management jigsaw puzzle. We summarise the innovation typologies found in the literature to two broad approaches by which companies attempt to innovate: undertaking incremental or radical innovation efforts. The former seeks to introduce changes that lie close to the current offerings and processes of an organisation; the latter aims to pursue objectives that lie more distant to the current organisational undertakings. We posit that risk management practises should be aligned with the type of innovation companies pursue, and question whether it is this misalignment that might explain the original puzzle. We argue that traditional risk management approaches cope well with incremental innovation. But radical innovation requires a different risk management approach. We conclude with a novel framework for risk management suitable for radical innovation and discuss the managerial implications.