Since Anderson's seminal paper published in 1958, it is known that sufficiently strong disorder can cause the localization of noninteracting quantum particles, inducing insulating behavior in macroscopic systems. Understanding the effects due to interactions in Anderson localized systems has been a major challenge ever since. In this talk I will review some recent studies we performed on the Anderson localization of atomic Fermi gases exposed to the correlated disorder created using optical speckle patterns, or to the quasi-disordered potentials created using bichromatic optical lattices. We employ theoretical concepts familiar form quantum chaos and random matrix theories for noninteracting systems, as well as quantum Monte Carlo simulations - combined with so-called modern theory of the insulating state - for interacting gases. If time permits, I will also highlight some recent results based on time-dependent density functional theory aiming at exploring the many-body localized transition in the cold-atom setup.