This paper presents a comprehensive review of the state-of-the-art constitutive models for frozen soils, focusing on their application under static and dynamic loading conditions. Frozen soils exhibit distinct mechanical behaviors compared to unfrozen soils due to the presence of ice, temperature dependency, time dependency, heterogeneity, and ice content. These characteristics make the development of accurate constitutive models challenging. The review summarizes various constitutive models, their underlying theories, advantages, and limitations. It also discusses the challenges and future research directions in frozen soil modeling, including the development of open databases and unified constitutive models using advanced techniques. The paper categorizes constitutive models into empirical models, elastoplastic models, viscoplastic models, hypoplastic models, binary element models based on homogenization theory, hyperplastic models, and thermo-poromechanics-based models. Each model is discussed in terms of its ability to capture the unique mechanical behaviors of frozen soils, including creep, time-dependent deformation, and the effects of temperature and ice content. The review highlights the importance of considering the complex interactions between ice, unfrozen water, and soil particles in frozen soils. It also emphasizes the need for models that can accurately predict the mechanical behaviors of frozen soils under various conditions, including the impact of temperature, stress, and ice content. The paper concludes that while numerous constitutive models have been proposed, few can comprehensively account for the unique characteristics of frozen soils. Future research should focus on developing more accurate and comprehensive models that can effectively describe the mechanical behaviors of frozen soils, including the thermo-hydro-mechanical (THM) coupled processes. The review aims to provide a better understanding of the mechanisms governing the multi-physical field coupling of frozen soils and offer valuable references for engineering design and maintenance.This paper presents a comprehensive review of the state-of-the-art constitutive models for frozen soils, focusing on their application under static and dynamic loading conditions. Frozen soils exhibit distinct mechanical behaviors compared to unfrozen soils due to the presence of ice, temperature dependency, time dependency, heterogeneity, and ice content. These characteristics make the development of accurate constitutive models challenging. The review summarizes various constitutive models, their underlying theories, advantages, and limitations. It also discusses the challenges and future research directions in frozen soil modeling, including the development of open databases and unified constitutive models using advanced techniques. The paper categorizes constitutive models into empirical models, elastoplastic models, viscoplastic models, hypoplastic models, binary element models based on homogenization theory, hyperplastic models, and thermo-poromechanics-based models. Each model is discussed in terms of its ability to capture the unique mechanical behaviors of frozen soils, including creep, time-dependent deformation, and the effects of temperature and ice content. The review highlights the importance of considering the complex interactions between ice, unfrozen water, and soil particles in frozen soils. It also emphasizes the need for models that can accurately predict the mechanical behaviors of frozen soils under various conditions, including the impact of temperature, stress, and ice content. The paper concludes that while numerous constitutive models have been proposed, few can comprehensively account for the unique characteristics of frozen soils. Future research should focus on developing more accurate and comprehensive models that can effectively describe the mechanical behaviors of frozen soils, including the thermo-hydro-mechanical (THM) coupled processes. The review aims to provide a better understanding of the mechanisms governing the multi-physical field coupling of frozen soils and offer valuable references for engineering design and maintenance.