Despite a large experimental effort, so far no evidence for flavour-violating decays of charged leptonssuch as l_i -> l_jgamma and l_i -> l_jl_kl_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 ofWilson 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-> mue are much more constrained from low-energy experiments mu -> egamma than from the limits of current and future direct searches at high energy.