The anomalous magnetic moment of the muon g-2 has been measured and computed to very high precision of about 0.5 ppm. For more than a decade, a discrepancy has persisted between experiment and Standard Model prediction, now of about 3-4 sigma. The main uncertainty of the theory prediction is due to strong interaction effects. With improved input for hadronic vacuum polarisation, the subleading hadronic light-by-light (HLbL) contribution starts to dominate the theory error.
While some constraints from QCD exist, the calculation of the HLbL contribution to g-2 is plagued by a substantial model dependence. In this talk, I will present a dispersive approach to HLbL scattering, based on the fundamental principles of unitarity and analyticity. Our dispersive formalism recently allowed us to evaluate two-pion contributions including rescattering effects and it shows a path towards a data-driven determination of the HLbL contribution to g-2 of the muon.