Since Power Analysis on smart-cards was introduced by Paul Kocher [KJJ98], the validity of the model used for smart-cards has not been given much attention. In this paper, we first describe and analyze some different possible models. Then we apply these models to real components and clearly define what can be detected by power analysis (simple, differential, code reverse engineering...). We also study, from a statistical point of view, some new ideas to exploit these models to attack the card by power analysis. Finally we apply these ideas to set up real attacks on cryptographic algorithms or enhance existing ones.