  It has been shown by Voiculescu that important classes of square independent
random matrices are asymptotically free, where freeness is a noncommutative
analog of classical independence. Recently, we introduced the concept of
matricial freeness, which is similar to freeness in free probability, but it
also has some matricial features. Using this new concept of noncommutative
independence, we described the asymptotics of blocks and symmetric blocks of
certain classes of independent random matrices. In this paper, we present the
main results obtained in this framework, concentrating on the ensembles of
blocks of Gaussian random matrices.
