This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture on the principles underlying bistability in biochemical signaling networks, which are illustrated with examples from the literature. The lectures cover analog, or graded, versus digital, all-or-none, responses in cells, with examples from different types of biological processes requiring each. Rate-balance plots are introduced as a method for determining whether generic one-variable systems exhibit one or several stable steady states. Bifurcation diagrams are presented as a more general method for detecting the presence of bistability in biochemical signaling networks. The examples include an artificial toggle switch, the lac operon in bacteria, and the mitogen-activated protein kinase cascade in both Xenopus oocytes and mammalian cells. The second part of the lecture links the concepts of bistability more closely to the mathematical tools provided by dynamical systems analysis. The examples from the first part of the lecture are analyzed with phase-plane techniques and bifurcation analysis, using the scientific programming language MATLAB. Using these programs as a template, the assignment requires the students to implement a model from the literature and analyze the stability of this model's steady states.