In his paper [5], Hamilton introduced the Ricci flow equation in order to prove that a compact three-manifold admitting a Riemannian metric of positive Ricci curvature is a spherical space form. In case of dimension four, Hamilton showed in [6] that compact four-manifold with positive curvature operator are spherical space form as well. Furthermore, Hamilton conjectured that in all dimensions compact Riemannian manifolds with positive curvature operators must be space forms. In this thesis, we give a survey of a recent resolution of this conjecture by $B\ddot{o} em$ and Wilking in [7] and some applications.