Opinion-dynamics models study how opinions evolve as dynamical processes on networks. Traditionally, these models have treated time as either discrete or continuous, operating under deterministic assumptions. However, real-world social interactions and opinion updates often exhibit randomness in time. In this talk, we propose a novel approach to incorporate random-time interactions by modeling them as renewal processes on networks. Through this framework, we derive corresponding opinion-dynamics models that capture the stochastic nature of social interactions. Notably, when renewal processes exhibit non-Poisson interevent statistics, the resulting opinion models naturally yield non-Markovian dynamics. These memory-dependent effects offer insights into various phenomena (such as stereotypes) observed in social and information sciences.