  We investigate simplified models of new physics that can accommodate the
measured value of the anomalous magnetic moment of the muon and the relic
density of dark matter. We define a set of renormalizable, SU(2)$\times$U(1)
invariant extensions of the Standard Model, each comprising an inert $Z_2$-odd
scalar field and one or more vector-like pairs of colorless fermions that
communicate to the muons through Yukawa-type interactions. The new sectors are
classified according to their transformation properties under the Standard
Model gauge group and all models are systematically confronted with a variety
of experimental constraints: LEP mass bounds, direct LHC searches, electroweak
precision observables, and direct searches for dark matter. We show that
scenarios featuring only one type of new fermions become very predictive once
the relic density and collider constraints are taken into account, as in this
case $g-2$ is not enhanced by chirality flip. Conversely, for models where an
additional source of chiral-symmetry violation is generated via fermion mixing,
the constraints are much looser and new precision experiments with highly
suppressed systematic uncertainties may be required to test the parameter
space.
