Models of the dark matter have been extensively studied, perhaps the best known example is the WIMP scenario, with abundance set by its weak scale interaction. In this talk, I will introduce the forbidden dark matter paradigm, where dark matter is a thermal relic that annihilates into heavier states in the early Universe. An exponential hierarchy between the DM mass and the electroweak scale follows from the exponential suppression of the thermally averaged cross section. If DM annihilates into unstable dark photons, the model is testable through large DM self-interactions and direct detection. If DM annihilates into SM leptons, this mechanism precisely predicts the DM mass is close to the mass of the SM particles that dominate the annihilation rate, with a relative mass splitting smaller than O(1). In this case, we show that most of the relevant parameter space can be covered by the next generation of proposed beam-dump experiments and the g-2 measurements.