In order to search for dark matter with increased sensitivity, the new generation of direct detection experiments will soon be operational with an increased target size (e.g. LZ with approximately 5 tons of LXe) and lower experimental thresholds (e.g. SuperCDMS in the high-voltage operation mode). While these features will certainly help further narrowing down the parameter space of weakly-interacting massive particles, they also offer the possibility of probing less canonical candidates for dark matter, as well as other types of new physics in the neutrino sector. In this talk I will review the different possibilities that this offers, including a recent example from 2006.11225, in which a light mediator in a gauged U(1)(L\mu-L\tau) could explain the discrepancy in the muon anomalous magnetic moment.
