Explore interacting stochastic processes on random graphs in this AAAS-AMS Invited Address from the 2022 Virtual Joint Mathematics Meetings. Delve into discrete time contact processes, continuous time models, voter models, and spike train models. Examine neuronal hox models, coupled oscillators, and the evolution of stochastic processes. Investigate classical limit theorems, weak convergence, empirical measures, and Wiener measure. Analyze weak interactions in dense graphs and sparse regimes, addressing challenges and counterexamples. Study local convergence, autonomous characterization, and unimodular roots in discrete time processes.