The anomalous magnetic moment of the muon is one of the prime physical quantities both to test the Standard Model at quantum loop level and to monitor the signals coming from physics beyond the Standard Model. After the first released results from the muon g-2 experiment at Fermilab solidifying the tension with the theory prediction, we take this occasion to discuss the dispersive analysis of some hadronic vacuum polarisation and hadronic light-by-light scattering contributions to the anomalous magnetic moment of the muon.