Spreading (diffusion) of new products is a classical problem. Traditionally, it has been analyzed using the compartmental Bass model, which implicitly assumes that all individuals are homogeneous and connected to each other. To relax these assumptions, research has gradually shifted to the more fundamental Bass model on networks, which is an agent-based model for the stochastic adoption decision of each individual. In this talk, I will present the emerging mathematical theory for the Bass model on networks. The main focus will be on the effect of network structure. For example, which networks yield the slowest and fastest adoption? I will also discuss the effect of heterogeneity among individuals: Does it always slow down the adoption? Can it be neglected?