Initially isotropic aggregates of crystalline grains develop anisotropic mechanical properties when undergoing large plastic deformations due to reorientation of the individual crystal lattices. This texture-induced anisotropy strongly alters the elastic, as well as inelastic, macroscopical behaviour, so that predicting the texture-evolution and the emerging anisotropic material behaviour is of special interest for practical applications. Towards the goal of simulating these processes, efficient homogenization methods are required to describe the interaction between the materials microstructure and its macroscopic properties. In this talk we present an implementation for simulating the crystallographic texture evolution of FCC polycrystals. First we discuss the behaviour of a single crystal under large deformation, comparing different approaches for integrating the flowrule for the plastic deformation gradient. We then proceed to homogenize the behaviour of the crystal aggregate to obtain the macroscopic properties. Here, special attention is given to the compatible grain-interaction of adjacent single crystals at their shared grain boundary. Next, we show several numerical examples for varying deformation histories, present the obtained discrete orientation distribution of the crystal aggregate and discuss the anisotropic macroscopic behaviour. Lastly, the numerical predictions are compared with experimental data of rolled aluminum with differing initial textures.