Human-robot object handovers have been an actively studied area of robotics over the past decade; however, very few techniques and systems have addressed the challenge of handing over diverse objects with arbitrary appearance, size, shape, and rigidity. In this paper, we present a visionbased system that enables reactive human-to-robot handovers of unknown objects. Our approach combines closed-loop motion planning with real-time, temporally-consistent grasp generation to ensure reactivity and motion smoothness. Our system is robust to different object positions and orientations, and can grasp both rigid and non-rigid objects. We demonstrate the generalizability, usability, and robustness of our approach on a novel benchmark set of 26 diverse household objects, a user study with naive users (N=6) handing over a subset of 15 objects, and a systematic evaluation examining different ways of handing objects. More results and videos can be found at https://sites.google.com/nvidia.com/ handovers-of-arbitrary-objects.