Augmented Reality (AR) holds the potential to revolutionize surgical procedures by allowing surgeons to visualize critical structures within the patient's body. This is achieved through superimposing preoperative organ models onto the actual anatomy. Challenges arise from dynamic deformations of organs during surgery, making preoperative models inadequate for faithfully representing intraoperative anatomy. To enable reliable navigation in augmented surgery, modeling of intraoperative deformation to obtain an accurate alignment of the preoperative organ model with the intraoperative anatomy is indispensable. Despite the existence of various methods proposed to model intraoperative organ deformation, there are still few literature reviews that systematically categorize and summarize these approaches. This review aims to fill this gap by providing a comprehensive and technical-oriented overview of modeling methods for intraoperative organ deformation in augmented reality in surgery. Through a systematic search and screening process, 112 closely relevant papers were included in this review. By presenting the current status of organ deformation modeling methods and their clinical applications, this review seeks to enhance the understanding of organ deformation modeling in AR-guided surgery, and discuss the potential topics for future advancements.