Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. I will describe recent work in which the parameter-free methods of chemical reaction network theory were employed in a comprehensive in silico search for bistable network topologies among more than 40,000 simple two-gene circuits. In addition to the identification of a large number of previously unknown bistable switches, our results highlight the potential usefulness of parameter-free modeling to the study of network evolution, and are suggestive of a role in the development of novel synthetic biological switches.