Despite a large experimental effort, so far no evidence for flavour-violating decays of charged leptons such as $l_i\to l_j��$ and $l_i\to l_j l_k l_k$ has been found. The absence of a signal puts very severe constraints on many extensions of the Standard Model. Here we apply a model independent approach by studying such decays in the Standard Model effective field theory. Going beyond leading order in the Standard Model couplings and considering all dimension 6 operators that might lead to lepton-flavour violation, we are able to extract limits on a large number of Wilson coefficients of such operators. We are also able to compare the impact of particular searches and find, for example, that flavour-violating decays of the $Z$-boson $Z\to ��e$ are much more constrained from low-energy experiments $��\to e ��$ than from the limits of current and future direct searches at high energy.

7 pages, 5 Tables; to appear in the Proceedings of the FCCP2015 Workshop