I’ll give a very informal presentation of CMPS for relativistic quantum field theories, explaining 1) “the old stuff”: how it works for phi^4 theory, how one does computations with it, why it makes sense from an entanglement entropy point of view. 2) “the new stuff”: how it can be applied to more complicated models (e.g. complex scalar field), more complicated observables, in particular defects (just on arxiv), and finally discuss the open problems related to less renormalizable potentials.