This paper reviews how competition authorities have incorporated innovation as part of their assessment in enforcement cases. It explores scenarios that have considered innovation from a static perspective, mostly analysing current and potential competition in well-identified product markets (incentives-based approach), as well as scenarios that have considered innovation from a dynamic perspective, often defining innovation markets (impact-based approach). It also looks at cases that have considered increases in innovation as potential justifications for decreases in competition. This note reviews how these different approaches have shaped market definition, the theories of harm considered, and even the design of remedies and commitments.