•The experimental validation and numerical applications were reviewed for moisture separator modeling.•The advantage and disadvantage of Eulerian-Eulerian and Lagrangian-Eulerian methods were compared.•An optimization design of moisture separator was performed by numerical modeling. The applications of numerical simulation can provide detailed information about the droplet behaviors that is useful to study the performance of the system of Moisture Separator (MS). In this study, the simulation results and new findings of MS modeling are reviewed under the framework of both Eulerian-Eulerian (EE) and Lagrangian-Eulerian (LE) methods. In addition, the experimental work on MS performance since the 1980s is carefully examined. First, we analyze the experimental test of the working performance of the most commonly used MS. The flow pattern, structure design, separation efficiency and pressure drop by the experiment work are summarized. Second, we provide the simulation findings of flow patterns, like droplet generation, droplet collision and droplet-wall impaction under the framework of the LE method. Third, we systematically show the simulation results of the droplet and the steam velocity field, void fraction distribution, separation efficiency and pressure drop. We find that the EE method is efficient to study a relative large scale of MS, such as swirl-vane separator. For the LE method, we find that the entire life of a droplet is easily to be tracked. Further, we verify that the accuracy of simulated separation efficiency of a mini-type cyclone can be increased by using the droplet collision model. Moreover, we introduce the simulation result of a separation system, which proves that numerical methods could be applied to optimize the design of MS for commercial market. Finally, the study concludes with the future directions needed to develop both EE and LE methods for MS modeling.