We present some Poisson process approximation results for stabilizing functionals of Poisson (or Binomial) processes that arise in stochastic geometry. Our bounds are derived for the Kantorovich-Rubinstein distance between a point process and an appropriate Poisson point process. We will discuss application to largest k-nearest neighbour distances. This is based on a joint project with Omer Bobrowski (Technion) and Matthias Schulte (Hamburg Institute of Technology) [see arXiv:2104.13261].