Pushed by the proliferation of antennas and of multiuser scenarios, matrices with random entries are appearing more and more frequently in information theory. This leads to the study of matrix channels, where the capacity depends on the distribution of the matrix's eigenvalues. These eigenvalues are complicated functionals of the entries of the matrix and the challenge lies therein. It is often the case that in order to better model different communication scenarios, one is driven away from matrix models typically studied in pure mathematics and physics. One cannot simply resort to the standard tools developed over the years in these fields and must come up with new approaches. In this thesis, our goal is to obtain results in scenarios where the randomness is limited by the nature of the channel, in order to widen applicability in real life scenarios.