Building mathematical models of cellular networks lies at the core of systems biology. It involves, among other tasks, the reconstruction of the structure of interactions between molecular components, which is known as network inference or reverse engineering. Information theory can help in the goal of extracting as much information as possible from the available data. A large number of methods founded on these concepts have been proposed in the literature, not only in biology journals, but in a wide range of areas. Their critical comparison is difficult due to the different focuses and the adoption of different terminologies. Here we attempt to review some of the existing information theoretic methodologies for network inference, and clarify their differences. While some of these methods have achieved notable success, many challenges remain, among which we can mention dealing with incomplete measurements, noisy data, counterintuitive behaviour emerging from nonlinear relations or feedback loops, and computational burden of dealing with large data sets.