The category of smooth manifolds and smooth maps does not have many desirable properties; it is neither (co)complete nor has a closed monoidal structure. Generalized smooth spaces are generalizations of smooth manifolds which permit many of those desirable categorical properties. There are several different models for generalized smooth spaces; such as, Chen Spaces, Sikorski's differential modules, stratifolds, diffeological spaces, Frölicher spaces, etc. In this talk we are interested in the categories of diffeological spaces, Frölicher spaces and formal duals of smooth algebras. We first briefly discuss some of the existing homotopy theories on these categories (e.g., homotopical structures on diffeological spaces by Chritiensen&Wu, by Haraguchi&Shimakawa, and by Kihara), and then we introduce a new collection of homotopical structures on them; either by using appropriate adjunctions or by using enrichments over other homotopical theories. Finally we compare some of these new homotopical structures with the already existing ones in the literature.