Abstract: After introducing rapidly the context of diffeology, I'll try to review some of the main constructions and show, through examples, how this differential geometry treat objects which do not belong to the classical category of manifolds. I will show also how using diffeology some classical theorems are dramatically simplified, and extended, in particular in de Rham calculus. I may also, if I have the time, introduce the program of symplectic diffeology: results, questions and perspectives.