  In recent years, the anomalous magnetic moment of the muon has triggered a
lot of activity in the lattice QCD community because a persistent tension of
about $3.5~\sigma$ is observed between the phenomenological estimate and the
Brookhaven measurement. The current best phenomenological estimate has an
uncertainty comparable to the experimental one and the error is completely
dominated by hadronic effects: the leading order hadronic vacuum polarization
(HVP) contribution and the hadronic light-by-light (HLbL) scattering
contribution. Both are accessible via lattice simulations and a reduction of
the error by a factor 4 is required in view of the forthcoming experiments at
Fermilab and J-PARC whose results, expected in the next few years, should
reduce the experimental precision down to the level of $0.14~$ppm. In this
article, I review the status of lattice calculations of those quantities,
starting with the HVP. This contribution has now reached sub-percent precision
and requires a careful understanding of all sources of systematic errors. The
HLbL contribution, that is much smaller, still contributes significantly to the
error. This contribution is more challenging to compute, but rapid progress has
been made on the lattice in the last few years.
