Bratteli diagrams are closely related to AF algebras and provide a convenient description of privileged states such as traces and Gibbs states. In view of applications to random walks on locally compact groups and groupoids, I shall define topological Bratteli diagrams. Markov measures will be identified as a class of quasi-invariant measures. The Poisson boundary of a random walk can be studied in this context. This is a work in progress with T. Giordano.