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 ∝ Q/ω, with Q and ω 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.arXiv:1903.08590v1 [cond-mat.mes-hall]

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