Anderson localization of ultra-cold atoms in speckle potentials is attracting considerable attention. Beyond the mere exciting opportunity to directly observe a localized wave function, the situation turns out to be very rich, from both experimental and theoretical points of view. For instance, there exists effective mobility edges as predicted by a theoretical analysis and observed in experiments. This is related to the fact that the speckle potential, although a non Gaussian process with an asymmetric probability distribution, actually derives from an electric field that is a Gaussian random process. Moreover, precise control of correlation functions in speckle potentials offer new possibilities to precisely study the problem of Anderson localization.