  The anomalous magnetic moment of the muon displays a $4.2\sigma$ tension with
the Standard-Model prediction, if $e^+e^-\to \text{hadrons}$ data are used for
hadronic vacuum polarization. In these proceedings we review possible
explanations of this anomaly in terms of heavy new particles. As the necessary
effect is of the order of the electroweak Standard-Model contribution, viable
explanations with TeV-scale physics must involve an enhancement factor; in
particular, one can obtain the chirality flip of the dipole operator via a
sizable coupling to the Higgs doublet instead of the small muon Yukawa
coupling. Such Standard-Model extensions then also predict effects in Higgs and
$Z$-boson decays to muons, with details depending on the $SU(2)_L\times U(1)_Y$
representations of the new particles. We first review the general case of
chirally enhanced new physics, before discussing in more detail the concrete
example of leptoquark models.
