In the Standard Model, rare charm decays have tiny, almost unobservable, branching ratios. Any discrepancy from its predictions can be used to enhance our comprehension of additional contributions and, eventually, lead to New Physics. The BESIII experiment profits from the clean environment of its leptonic collisions to search for rare decays in charm mesons and charmonium decays. In this presentation, a general review of the BESIII results in these searches will be discussed, with a focus on three main areas: FCNC decays, $J/\psi$ weak decays, and forbidden processes.