Although the Ricci flow with surgery has been used by Perelman to solve the Poincar�© and Geometrization Conjectures, some of its basic properties are still unknown. For example it has been an open question whether the surgeries eventually stop to occur (i.e. whether there are finitely many surgeries) and whether the full geometric decomposition of the underlying manifold is exhibited by the flow as $t \to \infty$. In this talk I will show that the number of surgeries is indeed finite and that the curvature is globally bounded by $C t^{-1}$ for large $t$. This confirms a conjecture of Perelman. Using the new curvature bound, it is possible to give a more precise geometric picture of the long-time behavior of the flow.