  Recent work of Belinschi, Mai and Speicher resulted in a general algorithm to
calculate the distribution of any selfadjoint polynomial in free variables.
Since many classes of independent random matrices become asymptotically free if
the size of the matrices goes to infinity, this algorithm allows then also the
calculation of the asymptotic eigenvalue distribution of polynomials in such
independent random matrices. We will recall the main ideas of this approach and
then also present its extension to the case of the Brown measure of
non-selfadjoint polynomials.
