Title: Recent results on Fano varieties. Abstract: In this talk we present some recent results on complex smooth Fano varieties. To this end, we first recall an invariant introduced by Casagrande, called Lefschetz defect. We review the literature to deduce that all Fano manifolds with Lefschetz defect greater than three are well known. Then we focus on the case in which the Lefschetz defect is equal to three, by discussing a structure theorem for such varieties. As an application, we use this result to classify all Fano 4-folds with Lefschetz defect equal to three: there are 19 families, among which 14 are toric. This is a joint work with C. Casagrande and S. Secci.