In a chemical reaction system, the concentrations of chemical species evolve in time, governed by the polynomial differential equations of mass-action kinetics. This talk provides an introduction to chemical reaction network theory, and gives an overview of algebraic and combinatorial approaches to determining whether a chemical reaction network admits multiple steady states. In general, establishing the existence of (multiple) steady states is challenging, as it requires the solution of a large system of polynomials with unknown coefficients. However, for networks that have special structure, various easy criteria can be applied. This talk will highlight results from Deficiency Theory (due to Feinberg), criteria for multistationarity for chemical reaction systems whose steady states are defined by binomial equations (in joint work with Carsten Conradi, Mercedes Pérez Millán, and Alicia Dickenstein), and a classification of small multistationary chemical reaction networks (in joint work with Badal Joshi).