Continuous Fiber Reinforced Composites (CFRCs) are extensively employed in advanced industries such as aerospace and rail transit, owing to their superior mechanical properties. In recent years, additive manufacturing (3D printing) has emerged as a primary method for fabricating CFRCs, eliminating the limitations of traditional manufacturing processes that rely on molds. This review provides a comprehensive overview of the latest advancements in predictive modeling of CFRCs additive manufacturing, covering the entire technological development pathway from process modeling to structural mechanics modeling of 3D printed CFRCs. The section on process modeling of CFRCs additive manufacturing explores key aspects such as resin flow and infiltration behavior, heat transfer mechanisms, residual stress evolution, and fiber misalignment control. The subsequent section on structural mechanics modeling of 3D printed CFRCs presents mainstream modeling approaches at the micro, meso, and macro scales, highlighting their application scenarios. It also examines the potential of multiscale modeling techniques, which bridge these different scales to enhance predictive accuracy. Finally, this review systematically identifies the major challenges currently faced in predictive modeling of CFRCs additive manufacturing and outlines future research directions. These insights provide theoretical guidance and technical support for advancing the scientific understanding and practical application of high-performance CFRCs in additive manufacturing.