The aim of this paper is to give an overview of Stein's method, which has turned out to be a powerful tool for estimating the error in normal, Poisson and other approximations, especially for sums of dependent random variables. We focus on the normal approximation of random variables posessing decompositions of Barbour, Karonski, and Rucinski (1989), which are particularly useful in combinatorial structures, where there is no natural ordering of the summands. We highlight two applications: Nash equilibria and linear rank statistics.