Geodetic measurements of crustal deformation over large areas deforming at slow rates (<5 mm/yr over more than 1000 km), such as the Western Mediterranean and Western Europe, are still a challenge because (1) these rates are close to the current resolution of the geodetic techniques, (2) inaccuracies in the reference frame implementation may be on the same order as the tectonic velocities. We present a new velocity field for Western Europe and the Western Mediterranean derived from a rigorous combination of (1) a selection of sites from the ITRF2000 solution, (2) a subset of sites from the European Permanent GPS Network solution, (3) a solution of the French national geodetic permanent GPS network (RGP), and (4) a solution of a permanent GPS network in the western Alps (REGAL). The resulting velocity field describes horizontal crustal motion at 64 sites in Western Europe with an accuracy on the order of 1 mm/yr or better. Its analysis shows that Central Europe behaves rigidly at a 0.4 mm/yr level and can therefore be used to define a stable Europe reference frame. In that reference frame, we find that most of Europe, including areas west of the Rhine graben, the Iberian peninsula, the Ligurian basin and the Corsica-Sardinian block behaves rigidly at a 0.5 mm/yr level. In a second step, we map recently published geodetic results in the reference frame previously defined. Geodetic data confirm a counterclockwise rotation of the Adriatic microplate with respect to stable Europe, that appears to control the strain pattern along its boundaries. Active deformation in the Alps, Apennines, and Dinarides is probably driven by the independent motion of the Adriatic plate rather than by the Africa-Eurasia convergence. The analysis of a global GPS solution and recently published new estimates for the African plate kinematics indicate that the Africa-Eurasia plate motion may be significantly different from the NUVEL1A values. In particular, geodetic solutions show that the convergence rate between Africa and stable Europe may be 30-60% slower than the NUVEL1A prediction and rotated 10-30°counterclockwise in the Mediterranean.