Centrifugal microfluidic platforms or lab-on-discs (LODs) have evolved into a popular technology for automating chemical and biological assays. LODs today enable scientists to implement and integrate different operational units, including fluid mixing, droplet generation, cell-sorting, gene amplification, analyte detection, and so forth. For an efficient design and cost-effective implementation of any microfluidic device, including LODs, theoretical analysis and considerations should play a more important role than they currently do. The theoretical analysis we will show is especially essential to the investigation of detailed phenomena at the small length scales and high-speed typical for LODs where a wide range of forces may be involved. Previous LOD review papers presented mostly experimental results with theory as an afterthought. Hence, a review paper focused on the theoretical aspects, and associated computational studies of LOD devices is an urgent need. In the present review paper, all previous computational studies on LOD devices are categorized as single-phase flows, two-phase flows, network simulation, and solids. For each of these categories, the governing equations and important formulas are presented and explained. Moreover, a handy scaling analysis is introduced to aid scientists when comparing different competing forces in LOD devices. We hope that by surveying and contrasting various theoretical LOD studies, we shed some light on existing controversies and reveal where additional theoretical work is needed.