Stein's method is used to get error bounds for distributional limit theorems in difficult settings with dependence. One variant of the method uses a distributional fixed point equation for the limit to create biased random variables that couple closely and give Kolmogorov error bounds. The preferential attachment random graph model is used in network science to model growth of networks where heavily connected nodes attract more future connections; this is a setting where there has been recent progress using this variant of Stein's method. I will survey some of this progress and give some new results in the multivariate approximation setting.