We shall first recall some basic results associated with Shannon classical information theory such as the notion of Information Capacity. We shall then extend this notion to some simple cases in the realm of quantum mesoscopic systems in order to compare it to other transport coefficients, such as electrical and thermal conductances. Then, we shall discuss further applications of the notion of Information Capacity to ensembles of antennas and to quantum systems such as the Full Counting Statistics of electrons and photons, the Casimir Effect, and other quantum vacuum effects.