I will review a series of works- in collaboration with M. Novaga and B. Ruffini on a variational model for charged liquid drops. Since the most natural formulation of this problem actually leads to non-existence of minimizers, a central question is the identification of regularizing mechanisms which restore well-posedeness. I will also present recent results obtained in collaboration with M. Novaga and A. Prade regarding the validity of Young's law for capillary charged drops.