This seminar deals with integrable models on graphs. After some motivations for studying such systems, I give the proof of the integrability of a Calogero model on a star graph (see J.Phys. A 40 (2007) 5491 and math-ph/0609057). I also discuss its symmetry. In particular, I emphasise the links with the complex reflection groups and twisted algebra. I finish with open problems in this quite recent domain of integrable models.