The ATLAS and CMS experiments have performed measurements of the $CP$ structure of the interaction between the Higgs boson and $\tau$ leptons using proton-proton collisions at $\sqrt{s}~=~13~{\rm TeV}$, delivered by LHC during 2016-2018. The measurements are based on the angular correlation between the decay planes of $\tau$ leptons produced in Higgs boson decays. The value of the effective mixing angle measured by ATLAS and CMS experiments are found to be $9 \pm 16^{\circ}$ and $-1 \pm 19^{\circ}$ at the $68\%$ CL, respectively. The data from ATLAS and CMS experiments disfavour the pure $CP$-odd hypothesis at $3.4$ and $3.0$ standard deviations, respectively. The results are compatible with expectations for the standard model Higgs boson.