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The Anderson models is a very popular example of a quantum system in a random external potential: it is used to describe conductivity/insulation phenomena in quantum systems. The bulk of modern mathematical research in this area focuses on proving the so-called localization when the spectrum of the Hamiltonian is pure point and the eigen-functions decay rapidly (e.g., exponentially). An important ingredient of the proof are the so-called Wegner-type estimates controlling accumulation of random eigen-values of a finite-vlume approximation to the Hamiltonian. In the talk I will report new results in this direction. It is a joint work with V Chulaevsky (University of Reims, France), to appear in the CMP. No preliminary knowledge of the subject will be assumed.