Search for $D^0\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $D^0\to \gamma \gamma$ at BaBar and BESIII

Three searches for rare decays of the charmed $D^0$ meson are presented: a search for $D^0\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ published by the BaBar collaboration using about 468 fb${}^{-1}$ of data and two searches for $D^0\to \gamma \gamma$, one published by the BaBar collaboration using about 470 fb${}^{-1}$ of data, and a second one presented as a preliminary result by the BESIII collaboration using approximately 2.9 fb${}^{-1}$. No statistically significant signal has been found, in agreement with the Standard Model predictions.