Light Mediator and Dark Matter Bound States: models and signatures

I discuss simple renormalizable models of dark matter which contains a light mediator that communicates interactions between the dark and standard model sectors. I first summarize the motivations and the current experimental constraints on this setup. The goal of this talk is to highlight a generic feature of such models that the light mediator can allow dark matter to form bound states. If the dark matter number density is due to an asymmetry in a conserved global quantum number, the bound states can be cosmologically stable. This scenario has several aspects in particle physics and cosmology that can be tested experimentally. I discuss in detail an example where the light mediator is a scalar particle.