We present two recent developments on lepton flavour violation in the MSSM. 1) The supersymmetric seesaw mechanism can be realized through the exchange of heavy SU(2)_W-triplet states, rather than `right-handed' neutrinos. In this scenario the ratio of the tau --> mu gamma (or tau --> e gamma) and mu --> e gamma rates are unambiguously predicted in terms of the low-energy neutrino parameters. 2) Lepton flavour violating decays of the Higgs bosons, (h, H, A) --> mu tau, are induced at one-loop level. The branching ratios can reach 10^{-4} for large tan(beta) and sizeable smuon-stau mixing. Interesting implications for LHC and correlations with tau --> mu gamma and tau --> 3 mu are found.