Within an effective field theory framework, we discuss the possibility to discriminate among different operators that contribute to lepton flavor violating (LFV) τ decays. Correlations among decay rates in different channels are shown to provide a basic handle to unravel the origin of LFV in these processes. More information about the underlying dynamics responsible for LFV can be gathered from differential distributions in three-body decays like τ→μππ or τ→3μ: these are considered in some detail. We incorporate in our analysis recent developments in the determination of the hadronic form factors for τ→μππ. Future prospects for the observation of LFV τ decays and its interpretation are also discussed.