Excess electrons from intrinsic defects, dopants and photoexcitation play a key role in many of the properties of TiO2. Understanding their behaviour is important for improving the performance of TiO2 in energy-related applications. We focus on anatase, the TiO2 polymorph most relevant in photocatalysis and solar energy conversion. Using first-principles simulations, we investigate the states and dynamics of excess electrons from different donors near the most common anatase (101) and (001) surfaces and aqueous interfaces. We find that the behaviour of excess electrons depends strongly on the exposed anatase surface, the environment and the character of the electron donor. Whereas no electron trapping is observed on the (101) surface in vacuo, an excess electron at the aqueous (101) interface can trigger water dissociation and become trapped into a stable surface Ti3+-bridging OH complex. By contrast, electrons avoid the (001) surface, indicating that oxidation reactions are favoured on this surface. Our results provide a bridge between surface science experiments and observations of crystal-face-dependent photocatalysis on anatase, and support the idea that optimization of the ratio between {101} and {001} facets could provide a way to enhance the photocatalytic activity of this material.