Although the Ricci flow with surgery has been used by Perelman to solve the Poincaré
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 times goes to infinity.

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. Using this curvature
bound it is possible to give a more precise picture of the long-time behavior of the
flow.