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In this talk we will present the computation of the Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras.We will introduce the Connes-Moscovici Hopf algebras and the Schwarzian Hopf algebra of noncommutative geometry, and we present our results on the Hopf-cyclic cohomology of these Hopf algebras. Finally, we will illustrate our computation calculating the generators of the Hopf-cyclic cohomology of the Schwarzian Hopf algebra. The talk is based on a joint work with B. Rangipour.