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.
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