Training visual control policies from scratch on a new robot typically requires generating large amounts of robot-specific data. How might we leverage data previously collected on another robot to reduce or even completely remove this need for robot-specific data? We propose a "robot-aware control" paradigm that achieves this by exploiting readily available knowledge about the robot. We then instantiate this in a robot-aware model-based RL policy by training modular dynamics models that couple a transferable, robot-aware world dynamics module with a robot-specific, potentially analytical, robot dynamics module. This also enables us to set up visual planning costs that separately consider the robot agent and the world. Our experiments on tabletop manipulation tasks with simulated and real robots demonstrate that these plug-in improvements dramatically boost the transferability of visual model-based RL policies, even permitting zero-shot transfer of visual manipulation skills onto new robots. Project website: https://edwardshu.com/rac