  We explore optical activity in thin films and bulk of type-I and type II Weyl
semimetals (WSM), and demonstrate the existence of a giant Kerr effect in both.
In time-reversal symmetry broken WSM thin films, the polarization rotation is
caused by the optical Hall conductivity including the anomalous Hall term. The
Kerr angle is found to be $\propto Q/\omega$, with $Q$ and $\omega$ being the
Weyl node separation and the optical frequency, respectively. In contrast, the
optical activity in the bulk WSM is dominated by axion electrodynamics, which
persists even in the Pauli blocked regime of no optical transitions. In bulk
WSM, $Q$ acts analogous to the magnetization in magnetic materials, leading to
large `polar Kerr effect' (linear in $Q$) when light is incident on WSM surface
without Fermi arc states, and the `Voigt effect' (quadratic in $Q$), when light
is incident on surface with Fermi arc states.
