This talk consists of two parts. In the first part, we will provide an overview of the importance of central limit theorems for functionals on point processes in the context of testing statistical hypotheses on spatial datasets. In the second part, we will focus on normal approximation for Gibbsian functionals. We will demonstrate how Stein’s method can be combined with a disagreement coupling of a Gibbsian functional and its Palm version. This will yield a central limit theorem if the underlying Gibbs process is dominated by a Poisson process with subcritical Boolean model. The talk is based on joint work with Anne Marie Svane (Aalborg).