In recent decades, laser additive manufacturing has seen rapid development and has been applied to various fields, including the aerospace, automotive, and biomedical industries. However, the residual stresses that form during the manufacturing process can lead to defects in the printed parts, such as distortion and cracking. Therefore, accurately predicting residual stresses is crucial for preventing part failure and ensuring product quality. This critical review covers the fundamental aspects and formation mechanisms of residual stresses. It also extensively discusses the prediction of residual stresses utilizing experimental, computational, and machine learning methods. Finally, the review addresses the challenges and future directions in predicting residual stresses in laser additive manufacturing.