  We study supersymmetric (SUSY) models in which the muon $g-2$ discrepancy and
the dark matter relic abundance are simultaneously explained. The muon $g-2$
discrepancy, or a 3$\sigma$ deviation between the experimental and theoretical
results of the muon anomalous magnetic moment, can be resolved by SUSY models,
which implies at least three SUSY multiplets have masses of
$\mathop{\mathcal{O}}(100)\, \mathrm{GeV}$. In particular, models with the
bino, higgsino and slepton having $\mathop{\mathcal{O}}(100)\, \mathrm{GeV}$
masses are not only capable to explain the muon $g-2$ discrepancy but naturally
contains the neutralino dark matter with the observed relic abundance. We study
constraints and future prospects of such models; in particular, we find that
the LHC search for events with two hadronic taus and missing transverse
momentum can probe this scenario through chargino/neutralino production. It is
shown that almost all the parameter space of the scenario can be probed at the
high-luminosity LHC, and a large part can also be tested at the XENON1T
experiment as well as at the ILC.
