  We study nonlinear magneto-optical responses of metals by a semiclassical
Boltzmann equation approach. We derive general formulas for linear and second
order nonlinear optical effects in the presence of magnetic fields that include
both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the
semiclassical approach (i) captures the directional anisotropy of linear
conductivity under magnetic field as a consequence of an anisotropic $B^2$
contribution, which may explain the low-field regime of recent experiments;
(ii) predicts strong second harmonic generation proportional to $B$ that is
enhanced as the Fermi energy approaches the Weyl point, leading to large
nonlinear Kerr rotation. Moreover, we show that the semiclassical formula for
the circular photogalvanic effect arising from the Berry curvature dipole is
reproduced by a full quantum calculation using a Floquet approach.
