Freely-acting discrete symmetries on Calabi-Yau three-folds can be used to form quotient Calabi-Yau manifolds with smaller Hodge numbers and a non-trivial first fundamental group. Such Calabi-Yau quotients are a crucial ingredient in realistic compactifications of the heterotic string. I will describe ongoing work and some progress towards classifying such discrete symmetries for Calabi-Yau hypersurfaces in toric four-folds, focusing on symmetries which can realised linearly on the toric ambient space.