These proceedings review the status of present and future bounds on muonic lepton flavour violating transitions in the context of an effective-field theory defined below the electroweak scale. A specific focus is set on the phenomenology of $\mu\to e\gamma$, $\mu \to 3e$ transitions and coherent $\mu\to e$ nuclear conversion in the light of current and future experiments. Once the experimental limits are recast into bounds at higher scales, the explorative power of such ``golden'' channels is presented.