  New physics in the lepton sector may account for neutrino masses, affect
electroweak precision observables, induce charged-lepton flavour violation, and
shift dipole moments. The low-energy predictions of different models are most
conveniently compared within the formalism of effective field theory. To
illustrate the benefits of this approach, we derive the Wilson coefficients for
a set of representative models: the fermionic seesaw mechanisms (type I and
III), the Zee model, and a minimal leptoquark model. In each case, the Weinberg
and the dipole operators have qualitatively different origins. In parallel, we
present the model-independent constraints on the Wilson coefficients coming
from various lepton observables. We then show that it becomes straightforward
to understand the allowed parameter space for each model, and to discriminate
between them. The Zee and leptoquark models are suitable to address the muon
$g-2$ anomaly. We also confront the models with the anomalies in the W-boson
mass and semileptonic $B$-meson decays.
