  Now that the Fermilab muon $g-2$ experiment has released the results of its
Run-1 data, which agrees with the results of the Brookhaven experiment, one can
examine the potential of simple extensions to explain the combined $4.2\sigma$
discrepancy between the SM prediction and experiment. This proceeding examines
a single-, two-, and three-field extension of the standard model and examines
their ability to explain the muon $g-2$ anomaly, and where possible, produce a
dark matter candidate particle with the observed relic density. This is based
on work carried out for Ref. [1]. It is found that one can only explain the
$a_\mu$ discrepancy whilst avoiding dark matter and collider constraints when
the contributions from BSM fields benefit from a chirality flip enhancement.
However, in general without small couplings and/or large masses, these models
can be heavily constrained by collider and dark matter experiments.
