Observables that violate lepton flavor symmetry are sensitive probes of physics beyond the Standard Model (BSM), since any observation would be a clear BSM signal. Limits on $\mu\to e$ conversion in nuclei are amongst the most stringent ones available, and are even expected to improve by up to four orders of magnitude at Mu2e and COMET. In this contribution, we presented a general effective-field-theory analysis, including an application that shows
how the spin-dependent $\mu\to e$ process already implies indirect limits on lepton-flavor-violating decays of light pseudoscalars that surpass direct limits by orders of magnitude. We also discussed the nuclear-structure input required for a robust interpretation of $\mu\to e$ conversion limits, in particular, uncertainties propagated from the nuclear charge distributions as well as uncertainty quantification for $\mu\to e$ overlap integrals.