In-hand object reorientation is necessary for performing many dexterous manipulation tasks, such as tool use in less structured environments, which remain beyond the reach of current robots. Prior works built reorientation systems assuming one or many of the following conditions: reorienting only specific objects with simple shapes, limited range of reorientation, slow or quasi-static manipulation, simulation-only results, the need for specialized and costly sensor suites, and other constraints that make the system infeasible for real-world deployment. We present a general object reorientation controller that does not make these assumptions. It uses readings from a single commodity depth camera to dynamically reorient complex and new object shapes by any rotation in real time, with the median reorientation time being close to 7 seconds. The controller was trained using reinforcement learning in simulation and evaluated in the real world on new object shapes not used for training, including the most challenging scenario of reorienting objects held in the air by a downward-facing hand that must counteract gravity during reorientation. Our hardware platform only used open-source components that cost less than 5000 dollars. Although we demonstrate the ability to overcome assumptions in prior work, there is ample scope for improving absolute performance. For instance, the challenging duck-shaped object not used for training was dropped in 56% of the trials. When it was not dropped, our controller reoriented the object within 0.4 radians (23°) 75% of the time.