The focus of this review is a comprehensive overview for the use of ab initio methods to deliver insight for AS-ALD with some notes on methods that are based on results from these methods (e.g., kMC). Reviews on other theoretical approaches (classical mechanics and coarse graining, classical nucleation theory, CFD, etc.) can be found elsewhere. Also the literature on other deposition processes like area-selective CVD is not covered. Note, that some of the AS-ALD principles explicated within this work, have been summarized before. Since modelling for such complex chemical phenomena requires close interplay to experimental studies, this fruitful interaction has also been covered before. Of course, the knowledge gained in this field often builds on insights gained from previous work on (non-area-selective) ALD. In this context several reviews are available, e.g., on the history of ALD, the principles of ALD, or on precursor design. The modelling aspects of ALD have also been summarized comprehensively. A very helpful database of manuscripts and reviews in the field of ALD has been compiled and is continuously updated. Recently, AS-ALD has become the focus of perspectives and overview articles. One perspective shows several crucial aspects for inhibitor selection in area-deactivation approaches and especially outlines for the first time clearly the importance of interaction between inhibitor and precursor. The surface chemistry perspective has been chosen in a more recent review on selection criteria for inhibitor-based AS-ALD. Also, the upcoming application of AS-ALD in industry has been summarized outlining the key role of modelling here. Shong et al. published a perspective on theoretical design strategies for precursors in AS-ALD showcasing what theory can bring to the field. What is still lacking is a comprehensive review of computational approaches to the field of AS-ALD outlining the perspectives and challenges which is the goal of this review.