Due to the complexity of analyzing residual stress, which involves numerous cutting parameters encompassing both mechanical and thermal stresses, various modeling and simulation methods, including analytical, numerical, and machine learning approaches have been summarized. An analytical model for predicting 2D orthogonal cutting and 3D milling residual stress is presented based on the cutting mechanism as well as the loading and unloading history of the stress field. The advancement in computational methods has prompted a review of finite element methods and mesh-free methods along with their principles, advantages, disadvantages, and application fields. Furthermore, machine learning models are employed to predict and control cutting residual stress based on data-driven approaches. These include support vector regression machines, artificial neural networks, and gradient boosted trees. A significant challenge for future work lies in addressing multi-scale size cutting residual stresses through hybrid methodologies.