  The purpose of this review article is to present some of the latest
developments using random techniques, and in particular, random matrix
techniques in quantum information theory. Our review is a blend of a rather
exhaustive review, combined with more detailed examples -- coming from research
projects in which the authors were involved. We focus on two main topics,
random quantum states and random quantum channels. We present results related
to entropic quantities, entanglement of typical states, entanglement
thresholds, the output set of quantum channels, and violations of the minimum
output entropy of random channels.
