In this work we show a numerical methodology for the resolution of compressible ows in both,structured and unstructured grids. The Moving Least Squares method (MLS) is used for the computation of the gradients and successive derivatives in a higherorder nite volume framework. Using the multiresolution properties of the MLS methodology, we dene a shock-detection methodology. This new methodology allows the extension of slope limiters to nite volume methods with order higher than two. We present some numerical examples that show the accuracy and robustness of the numerical method.