The photon-induced production of $\tau$ leptons has been measured by the CMS collaboration in both lead-lead and proton-proton collisions, at center-of-mass energies of $\sqrt{s_{NN}}=5.02$ TeV and $\sqrt{s}=13$ TeV, respectively. This was the first time such a process has been measured in proton-proton collisions. The results were also interpreted in terms of beyond-the-Standard-Model contributions to the anomalous electromagnetic moment of the $\tau$ lepton, setting the constraint $-0.0042 < a_\tau < 0.0062$ at 95% confidence level, improving the constraints set at LEP over 20 years ago.