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, the hadronic vacuum polarisation (HVP) and hadronic light-by-light (HLbL) contributions.
While the most precise HVP evaluation is based on dispersion relations and data input, HLbL is currently plagued by uncontrolled model uncertainties. Within a dispersive framework based on unitarity and analyticity, we scrutinize the uncertainty estimates for the two-pion HVP channel and we calculate model-independently two-pion contributions in HLbL, which shows an avenue towards a data-driven evaluation of g-2 of the muon.