Titol: The Self-Interaction revisited Abstract: We discuss the Self-Interaction problem in standard Density Functional Theory at the Local Density Approximation level. After a general presentation of the problem and of its relevance to numerous physcial and chemical problems we propose a clean reformulation of the Self Interaction Correction (SIC) both in static and dynamical problems. We introduce a double set of wavefunctions to describe the system and show that such a double set strategy is a key ingredient both for dynamics and for deriving efficient approximations of the full SIC approach. We show examples of applications in simple metal clusters and small organic molecules.