In crowding, the perception of an object deteriorates in the presence of nearby elements. Obviously, crowding is a ubiquitous phenomenon, since elements are rarely seen in isolation. Despite this ubiquity, there exists no consensus on how to model crowding. In previous experiments, it was shown that the global configuration of the entire stimulus needs to be taken into account. These findings rule out simple pooling models and favor models sensitive to global spatial aspects. In order to further investigate how to incorporate these aspects into models, we tested different types of texture segmentation models such as the Texture Tiling Model, a variation of the LAMINART neural model, a model based on Epitomes, a model based on filtering in the Fourier domain, and several classic neural network models. Across all models, simply capturing regularities in the stimulus does not suffice, as illustrated by a failure of the Fourier analysis model to explain our results. Importantly, we find that models with a grouping mechanism (such as the LAMINART model) work best. However, this grouping may be implemented in different ways, as we will show.