Polarizability is a key molecular property controlling induction and dispersion forces in molecules, and atomic polarizabilities in molecules are widely used elements both in qualitative schemes for understanding molecular interactions and in quantitative methods for modeling them. Unfortunately, experimental probes of local polarizability are not readily available. Here we predict the polarizability of individual atoms and functional groups in a variety of systems, and we draw both general and specific conclusions with broad consequences. We find that the polarizability of the same functional group (e.g., the carbonyl group) can differ substantially, depending on the position of this group in a molecule (e.g., in a protein). More specifically, we find that the polarizability of buried atoms and groups is screened and thereby diminished; thus the outermost atoms and functional groups (for example, those lying closer to the molecular van der Waals surface) are more polarizable than buried ones, even when acted on by the same electric field. These findings mitigate against attributing isolated system behavior to molecular fragments since their polarizability depends on their environment, and the methods used here provide a way to probe molecular polarizability with a finer grain than has previously been possible.