The most heavily used (quantum chemical) computational method in AS-ALD modelling is DFT. It provides a detailed description of the electronic structure and chemical reactivity but is efficient enough to handle systems of a few hundred atoms. This enables the ab initio description of surface chemistry which determines selectivity. This review now aims at summarizing the computational work in the field of AS-ALD with a focus on ab initio methods. It provides an overview for the non-specialist of which methods are available and which questions in AS-ALD can be targeted with those methods. A comprehensive overview of the literature is given together with a perspective on current developments and a "wish-list" of developments for the future. This will enable experts and non-experts alike to judge the suitability of using computational methods in their research in the field of AS-ALD. The aim is thus to broaden the already expanding scope of computational methods in this field and motivate researchers to use them where suitable. In the spirit of a previous review on computations in (nonarea-selective) ALD by Elliott, the emphasis is that the threefold aim of computational work to validate, explain and predict should be the target: Validating the accuracy of the computational methods, explaining experimental findings and ultimately moving on to predicting new chemistry in AS-ALD and thus contributing to further innovations in this field.