Neutrino masses, dark matter, cosmic matter-antimatter asymmetry constitute a clear evidence that new physics beyond the GWS Standard Model (SM) must exist. However, it is more and more uncertain whether such new physics is related to the electroweak symmetry breaking scale, hence being presumably present in the TeV region, or if it is part of new"dark sector" of particles communicating with the SM particles only via a suitable portal. I consider in my talk this latter possibility. I 'll discuss how the long-standing muon /g-2 /discrepancy as well as, more generally, the prospects of improved precision in measurements of lepton (magnetic and electric) dipole moments constitute an interesting ground where to test axion-like particles of such dark sector. I'll show that it is possible to have a simultaneous relevant role of light dark sector particles in the lepton dipole moments and in our quest to find an answer to the dark matter puzzle.