The standard model describes a vast number of particles and their decays, including those of the W and Z bosons. Even though a large fraction of such decays have been known for a long time and the respective branching fractions have been measured with great accuracy, there remain several rare processes that have never been observed or even experimentally probed. Their observation could help validate the theoretical frameworks commonly used to calculate their branching fractions, but also provide viable alternatives to measure fundamental properties of the vector bosons, and possibly offer hints of new physics beyond the standard model. The two general-purpose experiments at the LHC cover a rich program of rare decay searches. This report focuses on those in the electroweak sector, including the search for $\mathrm{W}^{\pm}\to\pi^{\pm}\gamma$ and $\mathrm{W}^{\pm}\to\pi^{\pm}\pi^{\pm}\pi^{\mp}$, performed by the CMS Collaboration, the measurement of the $\mathrm{Z}\to4\ell$ branching fraction, and the search for lepton flavor-violating decays $\mathrm{Z}\to\mathrm{e}/\mu\tau$, performed by the ATLAS Collaboration. Such searches and measurements exploit either partially or fully the integrated luminosity collected by the two experiments in the 2015--2018 data-taking period, and in some cases represent the state of the art in the respective fields.