  The non-observation of dark matter (DM) by direct detection experiments
suggests that any new interaction of DM with the Standard Model (SM) should be
very weak. One of the simplest scenarios to achieve this is a dark sector that
is charged under a new $U(1)_X$ symmetry, which is kinetically mixed with the
SM hypercharge $U(1)_Y$. We briefly review the status of such a minimal setup
and analyze in a second step how the picture is altered if also SM fields are
charged under the new symmetry. We exemplify this for the case of a gauged
$U(1)_{L_\mu-L_\tau}$ and show that this allows for a simultaneous explanation
of the $(g-2)_\mu$ excess and the DM relic abundance $\Omega_{DM}$.
Furthermore, we discuss the potential of four-lepton and two-lepton plus
missing energy signatures to test such scenarios.
