What enables proficient control of a brain-computer interface (BCI)? In this talk, I will argue that it is our ability to conceptualize a physical model of the device. First, I will present evidence that BCIs that correspond to simple physical systems are more readily controlled than those that do not. Next I will show that subjects compensate for sensory feedback delays during BCI control. This suggests that they may be building internal models – inner conceptualizations of device operation – that can be used to internally track the real-time position of the device. Finally, I will present results from a novel statistical analysis that allows us to extract subjects’ internal models from neural population activity at the resolution of tens of milliseconds. Mismatch between subjects’ internal models and the actual BCI explains roughly 65% of their movement errors, as well as long-standing deficiencies in BCI speed control. The neuroprosthetic control system thus provides a paradigm through which we may probe the brain’s ability to build abstract models of physical systems.