Abstract: Wave breaking is accompanied by the entrainment of air, forming mixed-phase turbulent flow with fully mixed air and water. The numerical simulation methods and closure model for mixed-phase turbulence are challenging topics in current research. This paper reviews the recent progress in numerical investigations of mixed-phase turbulence, with a focus on the numerical stability issues and solutions for high-density-ratio two-phase flow simulations. To address the numerical instability caused by the inconsistency between front-capturing and momentum equation discretization in traditional methods, the recently proposed density-prediction-synchronization method achieves stable computation under high-density-ratio conditions by explicitly solving the mass transport equation. Furthermore, the governing equations, spatiotemporal discretization schemes, and front-capturing techniques of this method are elaborated in detail, and its effectiveness is validated through classic test cases. Additionally, taking jet flow, wake flow, and bow wave breaking as examples, the flow characteristics of mixed-phase turbulence are analyzed, revealing the dominant influence of the Froude number on turbulent kinetic energy and turbulent mass flux. Regarding closure models, the advantages and limitations of algebraic and dynamic models are compared, highlighting that while dynamic models show greater theoretical potential, further research is needed to address the closure of combined terms. This study provides a systematic reference for the simulation and modeling of multiphase turbulence and outlines future research directions, such as establishing a standardized benchmark database and improving computational efficiency through GPU parallel optimization.