This thesis aims to fill this gap between static and dynamic risk measures. It presents a theory of dynamic risk measures based directly on classical, static risk measures. This allows for a direct connection of the static, the discrete time as well as the continuous time setting. Unlike the existing literature this approach leads to a interpretable pendant to the well-understood static risk measures. As a key concept the notion of divisible families of risk measures is introduced. These families of risk measures admit a dynamic version in continuous time. Moreover, divisibility allows the definition of the risk generator, a nonlinear extension of the classical infinitesimal generator. Based on this extension we derive a nonlinear version of Dynkins lemma as well as risk-averse Hamilton–Jacobi–Bellman equations.