In this talk we will discuss two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we will show that every small contravariant functor from spaces to spaces converting coproducts to products, up to homotopy, and taking homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors, see his [Calculus II, III] papers. The interpretation of the current result in terms of Homotopy Calculus is still a challenge. Homological representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets is equivalent to a restriction of a representable functor. This theorem is essentially equivalent to Goodwillie's classification of linear functors.