After a review (2002) of the fundamental constants of physics in the static limit (zero energy), we review the quantities whose ultraprecise knowledge is a key for testing the SM. Besides the Z mass, known to 20 ppm, one needs to know the fine-structure constant, alpha, evaluated at the weak scale (Mz), and the muon decay constant, Gmu. At higher order, the SM testing requires also the knowledge of the strong coupling constant, and of fermion masses, evaluated at the right scale. A pedagogical introduction, the summary of the developments of the last decade and the promises of ongoing and future programs will be given.
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