Creating a controllable and relightable digital avatar from multi-view video with fixed illumination is a very challenging problem since humans are highly articulated, creating pose-dependent appearance effects, and skin as well as clothing require space-varying BRDF modeling. Existing works on creating animatible avatars either to not focus on relighting at all, require controlled illumination setups, or try to recover a relightable avatar from very low cost setups, i.e. a single RGB video, at the cost of severely limited result quality, e.g. shadows not even being modeled. To address this, we propose Relightable Neural Actor, a new video-based method for learning a pose-driven neural human model that can be relighted, allows appearance editing, and models pose-dependent effects such as wrinkles and self-shadows. Importantly, for training, our method solely requires a multi-view recording of the human under a known, but static lighting condition. To tackle this challenging problem, we leverage an implicit geometry representation of the actor with a drivable density field that models pose-dependent deformations and derive a dynamic mapping between 3D and UV spaces, where normal, visibility, and materials are effectively encoded. To evaluate our approach in real-world scenarios, we collect a new dataset with four identities recorded under different light conditions, indoors and outdoors, providing the first benchmark of its kind for human relighting, and demonstrating state-of-the-art relighting results for novel human poses.