The advance of semiconductor technology not only enables integrated circuits with higher density and better performance but also increases their vulnerability to various aging mechanisms which occur from front-end to back-end. Analysis on the impact of aging mechanisms on circuits’ reliability is crucial for the design of reliable and sustainable electronic systems at advanced technology nodes. As one of the most crucial back-end aging mechanisms, electromigration deserves research efforts. This paper introduces recent studies on physics-based modeling of electromigration aging of on-chip interconnects. At first, the background of electromigration is introduced. The conventional method and physics-based modeling for electromigration are described. Then studies on how electromigration affects powers grids and signal interconnects are discussed in detail. Some of them focus on the comprehensiveness of modeling methodology, while others aim at the strategies for improving computation accuracy and speed and the strategies for accelerating/decelerating aging. Considering the importance of electromigration for circuit reliability, this paper is dedicated to providing a review on physics-based modeling methodologies on electromigration and their applications for integrated circuits interconnects.