Abstract: In this talk, I will discuss a scenario in which today's dark matter (DM) sector was a sector of conformal field theory (CFT) in the early universe. Since the conformal invariance prevents the existence of mass scale necessary for the dark "matter", it needs to be broken and I show that it can be achieved by a portal coupling to the SM. This portal interaction can produce the dark sector via the "Conformal Freeze-in (COFI)" mechanism. Generically, COFI predicts a light DM via a slow renormalization group running followed by a dynamical mass generation. Therefore, our scenario represents an interesting case in which today's dark matter was a bath of radiation and only later transformed into a matter thanks to a cosmological phase transition occured in the SM. I discuss systematically all possible portal couplings and emphasize the role of "operator mixing" effects. In one interesting case, I show that the dark photon can emerge as a composite vector meson in which there is a non-trivial correlation between the mass and the kinetic mixing. I will then describe relevant phenomenologies, including dark matter self-interaction, warm DM bound, and stellar cooling constraints.