I will discuss the phase structure of Yang-Mills matter at moderate temperature and chemical potential. Motivated by large Nc physics, I will argue that the non-perturbative structure of QCD can give rise to hitherto little explored phenomena, such as the coexistence of confinement with perturbative quark degrees of freedom. I will however show that this "quarkyonic phase" is defined by a percolation-type phase transition line which curves in "number of colors", as well as density and temperature. Given theoretical uncertainities in dealing with matter at this regime, therefore, a phenomenological and experimental investigation of matter at high chemical potential might be decisive to determine if the quarkyonic phase does in fact exist. I will conclude discussing possible experimental signatures of this new state of matter, concentrating on electromagnetic signals, as well as proposals for studying this matter using Gauge/Gravity duality.
