I will give an overview of the geometry of Fano 3-folds after Mori theory. After discussing past approaches to the classification, I will highlight why such attempts seem hopeless. Building on recent advances in the geometry of Fanos, I introduce a new viewpoint on the classification problem. A main emphasis will be given to the unpredicted behaviour of the first examples of non-complete intersection Fanos, discovered in a joint work with Takuzo Okada.