We consider the problem of fair resource allocation in a system where user demands are dynamic, that is, where user demands vary over time. Our key observation is that the classical max-min fairness algorithm for resource allocation provides many desirable properties (e.g., Pareto efficiency, strategy-proofness, and fairness), but only under the strong assumption of user demands being static over time. For the realistic case of dynamic user demands, the max-min fairness algorithm loses one or more of these properties. We present Karma, a new resource allocation mechanism for dynamic user demands. The key technical contribution in Karma is a credit-based resource allocation algorithm: in each quantum, users donate their unused resources and are assigned credits when other users borrow these resources; Karma carefully orchestrates the exchange of credits across users (based on their instantaneous demands, donated resources and borrowed resources), and performs prioritized resource allocation based on users' credits. We theoretically establish Karma guarantees related to Pareto efficiency, strategy-proofness, and fairness for dynamic user demands. Empirical evaluations over production workloads show that these properties translate well into practice: Karma is able to reduce disparity in performance across users to a bare minimum while maintaining Pareto-optimal system-wide performance.