System identification is an inference problem: given data, what can we infer about the data-generating system? In this talk I develop a Bayesian view of identification in which that inference is carried out as message passing on Forney-style factor graphs. The Kalman filter, RTS smoother, and recursive least squares estimator are all special cases of belief propagation on a Gaussian chain. But the same machinery extends to non-Gaussian, nonlinear, time-varying, and hierarchical models. The engine underneath is variational free-energy minimization, in which the intractable posterior is approximated by a tractable distribution through an upper bound on log model evidence. Constraining that distribution to factorize along the graph turns inference into a set of message updates, computed locally at factor nodes. This perspective does more than reproduce known estimators. Because the factor graph also computes local contributions to model evidence as a byproduct, it offers a principled approach to model selection and structure adaptation. Finally, computation can be triggered on incoming data, meaning beliefs are updated only when and where new information arrives. I demonstrate this kind of distributed event-driven inference on a worked example of online system identification.