QCD in the Veneziano limit, Nc->oo, Nf->oo, with x=Nf/Nc fixed, has been conjectured to have an interesting phase diagram, including a conformal window, a real QCD-like phase, and a conformal transition separating the two. We will describe recent efforts to construct holographic theories with behavior that is similar to QCD. At zero temperature we will establish the nature of the conformal phase transition, BKT scaling in the "walking region", and Efimov vacua. At finite temperature we will determine and explore the structure of the phase diagram as a function of x. WE will also study finite temperature and finite density, and we will find a familiar phase diagram and a surprise.