The description of material failure as an energy minimization problem, i.e., the Francfort–Marigo model, has been studied widely in recent years. The approximation of the crack surface as a phase field, i.e., smeared interface, enjoys great popularity, as it allows describing fracture as a set of partial differential equations. In numerical homogenization, FFT‐based solution methods have been established over the past two decades. Their purpose is to compute the overall response of a heterogeneous microstruture w.r.t. a macroscopic loading and can be applied to a variety of nonlinear materials. The benefits lie in a fast implementation and the possibility to use image data like CT‐scans as input without further need for meshing. Based on the results of the master thesis of the first author, we investigate phase field crack propagation on heterogeneous microstructures using FFT‐based solvers.