  An extended Higgs sector may allow for new scalar particles well below the
weak scale. In this work, we present a detailed study of a light scalar $S$
with enhanced coupling to leptons, which could be responsible for the existing
discrepancy between experimental and theoretical determinations of the muon
anomalous magnetic moment. We present an ultraviolet completion of this model
in terms of the lepton-specific two-Higgs doublet model and an additional
scalar singlet. We then analyze a plethora of experimental constraints on the
universal low energy model, and this UV completion, along with the sensitivity
reach at future experiments. The most relevant constraints originate from muon
and kaon decays, electron beam dump experiments, electroweak precision
observables, rare $B_d$ and $B_s$ decays and Higgs branching fractions. The
properties of the leptonic Higgs portal imply an enhanced couplings to heavy
leptons, and we identify the most promising search mode for the high-luminosity
electron-positron colliders as $e^+{+}e^-\to\tau^+{+}\tau^-{+}S \to
\tau^+{+}\tau^-{+}\ell{+}\bar \ell$, where $\ell =e,\mu$. Future analyses of
existing data from BaBar and Belle, and from the upcoming Belle II experiment,
will enable tests of this model as a putative solution to the muon $g-2$
problem for $m_S < 3.5$ GeV.
