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Bayesian networks and their variants are a prominent graphical representation of distributions over random variables with a wide range of applications in, e.g., data mining, robotics, speech recognition or systems biology. They succinctly represent full joint distributions using a directed acyclic graph to capture (in)dependencies between the variables. Dynamic Bayesian networks (DBN) serve to describe how the distributions evolve over time. Assuming a discrete time domain, DBNs thus represent sequences of distributions. While classical approaches for the analysis of DBNs focus on finite-horizon inference, the talk will be about verification problems for their long-run behavior defined by the induced infinite sequence of distributions.