In this talk we present local results for the Ricci flow. In dimension two we generalise G.Perelman's "Pseudolocality" result to allow cone like regions ( which are by definition not locally euclidean ). In higher dimensions we combine pseudolocality with local curvature bounds to study solutions on regions which are initially almost euclidean and have a lower bound on the curvature operator. In three dimensions we replace the fact that region is almost euclidean by the assumption that the possible rate of curvature blow up as time goes to zero is "natural".