Overview of classical and recent decidability and complexity results for networks of timed communicating automata

We present a journey into the study of timed communicating automata, a rich model of concurrency and communication incorporating timing features. We start from classic results for communicating automata (without time) giving intuitions on the basic techniques yielding decidability. We then move to the timed setting, pointing out why those techniques break and how to fix them. We conclude with recent results completely characterising the topologies yielding a decidable reachability problem in the general setting of timed channels. Based on joint work with F. Herbreteau, A. Stainer, and G. Sutre.