Residual stresses and distortions are the result of complex interactions between welding heat input, the material’s high-temperature response, and joint constraint conditions. Both weld residual stress and distortion can significantly impair the performance and reliability of welded structures. In the past two decades, there have been many significant and exciting developments in the prediction and mitigation of weld residual stress and distortion. This paper reviews the recent advances in the prediction of weld residual stress and distortion by focusing on the numerical modeling theory and methods. The prediction methods covered in this paper include a thermo-mechanical-metallurgical method, simplified analysis methods, friction stir welding modeling methods, buckling distortion prediction methods, a welding cloud computational method, integrated manufacturing process modeling, and integrated computational materials engineering (ICME) weld modeling. Remaining challenges and new developments are also discussed to guide future predictions of weld residual stress and distortion.