Abstract: Grasping objects of different shapes and sizes - a foundational, effortless skill for humans - remains a challenging task in robotics. Although model-based approaches can predict stable grasp configurations for known object models, they struggle to generalize to novel objects and often operate in a non-interactive open-loop manner. In this work, we present a reinforcement learning framework that learns the interactive grasping of various geometrically distinct real-world objects by continuously controlling an anthropomorphic robotic hand. We explore several explicit representations of object geometry as input to the policy. Moreover, we propose to inform the policy implicitly through signed distances and show that this is naturally suited to guide the search through a shaped reward component. Finally, we demonstrate that the proposed framework is able to learn even in more challenging conditions, such as targeted grasping from a cluttered bin. Necessary pre-grasping behaviors such as object reorientation and utilization of environmental constraints emerge in this case.