The anomalous magnetic moment of the muon is one of the most promising observables to identify hints for physics beyond the Standard Model. This observable has been measured with a precision of 0.5 ppm and exhibits a persistent discrepancy of 3.5 standard deviations with the theoretical prediction based on the Standard Model. The theory error is entirely dominated by uncertainties from the hadronic sector, namely the hadronic vacuum polarization and the hadronic light-by-light scattering. In this talk, I will present recent progress in calculating both contributions using lattice QCD simulations and discuss the challenges to match the experimental precision.