Powder Bed Fusion (PBF) is a growing and expanding technology for Additive Manufacturing (AM) of metallic materials. PBF has numerous advantages, including near-net-shaped parts, low tooling costs, and the ability to tailor microstructures, which make it an ideal candidate for manufacturing extremely complex designs that can be used in a variety of high-tech industries. Despite these enormous benefits, residual stress, and distortion, arising from a substantial cooling rate, temperature gradient in the melt pool and the layer-by-layer nature of the process, represent a challenge for the implementation of PBF technology in metal AM more broadly. Residual stress has a significant impact on the dimensional accuracy of printed parts and leads to severe defects such as cracks, delamination, and distortion. Conducting trial-and-error real AM build iterations to predict the developed residual stress and finding a strategy to mitigate its adverse effect is a time consuming, costly, and challenging process. Computational-based models offer an effective means to accurately predict residual stress, while reducing costs and saving time. This article discusses the fundamental principles underlying the numerical models used to predict residual stress. It investigates and presents their principles in a systematic manner, facilitating an in-depth understanding of these various numerical models. This deep investigation not only establishes a solid foundation for the improvement of existing models but also highlights the potential for the development of novel, more efficient numerical models for predicting residual stress in PBF. The review examines the experimental techniques used to validate these numerical approaches and clarifies how they can be used to validate residual stress prediction models. Furthermore, the potential application and integration of machine learning in conjunction with numerical models to predict residual stress and suggest effective mitigation strategies are also discussed. The review demonstrates how simulation can be used as an effective tool to efficiently identify suitable residual stress mitigation strategies in the PBF AM process.