Abstract: A classical problem in chemical reactor design can be stated roughly in the following way: Given a network of chemical reactions and a specified feed, how should one design a chemical reactor to enhance the production of certain desired species while suppressing the production of undesired ones? The purpose of this article is to describe recent work in which geometric control theory provides sometimes surprising answers to classical reactor design questions. As an example it is shown that, associated with a given reaction network (with kinetics) and a given feed composition, there are certain exceptional numbers -- something like eigenvalues -- having special significance for reactor design: A classical steady-state CFSTR design can have an optimal conversion relative to all other steady-state designs only if the CFSTR residence time assumes one of those exceptional values.