Stochastic geometry is the branch of probability theory dealing with spatial random structures such as random tessellations, random sets, random polytopes or spatial random graphs. Such objects are often constructed from underlying point samples. In many cases and also throughout this talk, it is assumed that these points are given by a Poisson process. Thus, quantities of interest are random variables depending only on a Poisson process, so-called Poisson functionals. Since random geometric structures and associated random variables usually exhibit an extremely complex behaviour, which does not admit explicit finite size descriptions, one studies the asymptotic behaviour as the number of underlying points tend to infinity. In order to establish central limit theorems for this situation, one is interested in approximating distributions of Poisson functionals by normal distributions. A powerful tool to establish such results is the Malliavin-Stein method, which will be discussed in this talk. It combines Stein's method, a collection of techniques to derive quantitative limit theorems, with Malliavin calculus, a variational calculus for random variables. To illustrate the use of the Malliavin-Stein method, some problems from stochastic geometry will be considered.