We shortly review and emphasize how l_j -> l_i gamma experiments and the searches for lepton e.d.m. are constraining New Physics model building. They are pure signals of new phenomena around the TeV scale since the SM contributions are definitely negligible. It is quite remarkable that they also give effective tests of the LFV & CPV in seesaw couplings and in grand-unified theories. In particular, the limits on d_e nicely complement the proton decay bounds in selecting O(10) models.
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