Precast concrete frame structures are widely adopted around the world due to their various advantages, so it is important to study their seismic performance. The development of damage mechanics has enabled us to accurately investigate the typical failure mechanisms of precast structures. This paper presents three of the most commonly used modeling approaches based on damage mechanics for analysis of precast reinforced concrete structures under cyclic loading and compares the performance of the three models. Particularly, the shear behavior of the joint panel and the bond-slip behavior of the beam–column interfaces are especially considered, which are the key issues for precast concrete structures. First, the fundamental assumptions, formulations, and modeling strategies are given in detail for each approach. Then, the unified damage mechanics for concrete is introduced, and the model for reinforcement bars and the consideration of the bond-slip effect are also presented. Several benchmark cyclic tests of precast beam-to-column connections are chosen to evaluate the accuracy and efficiency of the modeling approaches. The numerical results, e.g. the capacities, deformations, and energy dissipation of the connections, are compared to the experimental results to show the ability of each approach. With this study, we can gain a further understanding of the characteristics and applicability of each modeling approach, helping us make a better decision in choosing which modeling approach is appropriate.