  Initiated around the year 2007, the Malliavin-Stein approach to probabilistic
approximations combines Stein's method with infinite-dimensional integration by
parts formulae based on the use of Malliavin-type operators. In the last
decade, Malliavin-Stein techniques have allowed researchers to establish new
quantitative limit theorems in a variety of domains of theoretical and applied
stochastic analysis. The aim of this survey is to illustrate some of the latest
developments of the Malliavin-Stein method, with specific emphasis on
extensions and generalisations in the framework of Markov semigroups and of
random point measures.
