We present results on the comparison between experiments and theory on the bichromatic lattice for cold atoms gases. This setup allows us to study the physics of disordered bosons where superfluid, Mott and glass phases compete. We first review the model and its phase diagram obtained from numerical calculations. The localization mechanism, which is different from the one for uncorrelated disorder, is introduced and its possible experimental signatures are proposed. Then, experimental results covering the full range of the disorder vs interaction diagram are confronted to numerical results. The effect of the trapping potential and of temperature are analyzed to explain the observed momentum distribution. We conclude on ongoing experiments using a similar setup.