Authenticated Key Exchange (AKE) protocols are a core building block of all modern communications, connecting the distribution benefits of public-key cryptography to the performance benefits of symmetric-key cryptography. Modern AKE protocols are proven secure in game-based security models that offer considerably more security guarantees than the seminal Bellare-Rogaway model from 1993, in order to capture real-world security properties such as various notions of forward secrecy and resistance against predictable or bad pseudorandom number generators. For most of these security models, it is claimed that they offer “the best possible security”, based on informal arguments that at best hold under unstated assumptions. This has led to a fragmented landscape of AKE security models with seemingly contradictory results. We provide the first systematization of the limits of game-based security models for two-party AKE protocols. Our treatment covers classical stateless protocols as well as a restricted class of modern stateful protocols. Our analysis uncovers how the details of the considered protocol class have crucial implications for (im)possibility results, and reveals how different security goals can be achieved in different relevant classes of AKE protocols. From our formal impossibility results, we derive strong security models for these classes and give protocols that satisfy them.