The flavor changing neutral current (FCNC) and lepton number violation (LNV) processes in $D$ decays are very rare within the Standard Model and beyond the reach of current collider experiments. Any evidence of a signal in such decay processes would be a clear indication of new physics. The new physics models propose several weakly interacting light dark matter particles to explain the features of astrophysical observations. The possibility of such a low-mass invisible particles in different decay modes has recently been explored by several collider experiments. This report summarizes the current experimental status of the FCNC, LNV and invisible decays of D mesons.