Recent studies of photon-induced processes in ultraperipheral Pb–Pb and proton–proton collisions with the CMS detector play an important role in testing the Standard Model (SM) and probing potential new physics. The analysis of 𝛾𝛾 → 𝜏+𝜏− production enables CMS to set the most stringent limits to date on the anomalous magnetic moment of the 𝜏 lepton. Using the 𝛾𝛾 → 𝑊+𝑊− process, CMS has obtained stringent limits on anomalous quartic gauge couplings (aQGCs).