Several mechanisms have been suggested to explain the increasing stability of atrial fibrillation (AF) over time. Disruption of electrical coupling between muscle bundles, resulting in narrower and thus more fibrillation waves, is considered as one of the main mechanisms contributing to AF stability in structurally remodeled atria. Also, the anatomy of the atrial wall has been demonstrated to significantly determine conduction patterns during AF. Most of these mechanisms have been studied in several in silico studies. But more than that, there are experimental studies suggesting that the development of the substrate for AF goes along with increasing incidence of conduction from the sub-epicardial layer to the endocardial bundle network and vice versa. While these studies conclusively demonstrate transmural conduction in the atrial wall, they leave open several important conceptual questions. In particular this talk focuses on in silico modeling of three-dimensional conductions during AF and its effect on AF stability.