In this talk we give a new and elementary proof for the C^{2,alpha} regularity of solutions to the Monge-Ampere equation, which was first obtained by Calabi-Pogorelov, and later by Evans-Krylov. We will also establish the global C^{2,alpha} estimate for the second boundary value problem of the Monge-Ampere equation, which was obtained by Caffarelli and Delanoe-Urbas under stronger conditions on the domains and right hand side. We present a different proof under weaker conditions.