Abstract: Manifolds are very nice objects in modern mathematics. However, the category of manifolds is not that pleasant. Many generalizations of manifolds are proposed around 1980's. Diffeological spaces are one of them, which were first defined by J. Souriau in 1980, and later on systematically developed by P. Iglesias-Zemmour, J. Baez, A. Hoffnung and others. In this talk, some known results on the basic properties of diffeological spaces and some of their differential geometric and topological aspects will be described. Some new results on the general topological aspects and categorical aspects will be presented at the end.