In nature there are millions of distinct networks of chemical reactions that might present themselves for study at one time or another. Each new network gives rise to its own peculiar system of differential equations, and, to make matters worse, these systems are usually large and almost always nonlinear. Nevertheless, each reaction network induces its corresponding differential equations (up to parameter values) in a precise way. This raises the hope that, even for highly intricate networks, qualitative properties of the induced differential equations might be tied directly to aspects of reaction network structure Chemical reaction network theory aims to do just that. In particular, it aims to place in the hands of those unfamiliar with modern mathematics powerful tools for connecting reaction network structure to the capacity for various kinds of qualitative behavior. The theory has not been specific to biology, but, for obvious reasons, there is now growing interest in biological applications. Very recent work (with Gheorghe Craciun) has been dedicated specifically to biochemical networks driven by enzyme-catalyzed reactions. It is now known, for example,that there are remarkable and very subtle connections between properties of reaction diagrams of the kind that biochemists normally draw and the capacity for biochemical switching. My aim in this talk will be to explain, for an audience unfamiliar with chemical reaction network theory, some tools that have recently become available.