  The knowledge of the density matrix of a quantum state plays a fundamental
role in several fields ranging from quantum information processing to
experiments on foundations of quantum mechanics and quantum optics. Recently, a
method has been suggested and implemented in order to obtain the reconstruction
of the diagonal elements of the density matrix exploiting the information
achievable with realistic on/off detectors, e.g. silicon avalanche
photo-diodes, only able to discriminate the presence or the absence of light.
The purpose of this paper is to provide an overview of the theoretical and
experimental developments of the on/off method, including its extension to the
reconstruction of the whole density matrix.
