In a chemical reaction network, the concentrations of chemical species evolve in time, governed by the differential equations of mass-action kinetics. This talk provides an introduction to the algebraic study of chemical reaction network theory. Chemical reactions can be represented by directed edges of a graph. A basic question is whether such a network has a steady state. The locus of all steady states is defined by the steady state ideal. We introduce the space of toric dynamical systems of a digraph representing a chemical network. The nicest chemical reaction networks are the toric dynamical systems: their steady state loci and moduli spaces are toric varieties. In chemistry, they are the systems whose steady states are a special kind, called complex balancing steady states. We make the connection also to the deficiency theory of M. Feinberg. No prior knowledge of chemical reaction network theory or toric geometry will be assumed This is joint work with Gheorge Craciun, Alicia Dickenstein, and Bernd Sturmfels.