Frozen soil is the essential component of terrestrial cryosphere.Soil freeze-thaw process （SFT） affects soil structure， soil hydrothermal transfer， and biogeochemical processes， thereby influencing local and global weather and climate through land-atmosphere interaction.Therefore， it is of importance to explore SFT for human activities in frozen soil regions and for studying weather and climate change for local and remote regions.This paper reviews the effects and physical mechanisms of gravel and soil organic matter （SOM） on soil thermal and hydrological parameters and SFT， and summaries achievements in parameterizations of SFT， with focuses on soil thermal conductivity， hydraulic parameters， water-heat coupled parameterization， and freeze-thaw fronts.Gravel （SOM） has higher （lower） thermal conductivity and lower （higher） heat capacity， and thus they have different effects on the soil heat transfer and vertical distribution of soil temperature.Additionally， the existences of gravel and SOM change soil porosity， matrix capillary and adsorption， thereby affecting the transfer and vertical distribution of soil water content.Previous studies show that： （1） the Johansen scheme and its derivatives are widely incorporated into land models to calculate soil thermal conductivity.In consideration of the effect of gravel and SOM on soil thermal conductivity， the Balland-Arp scheme， a derivative of the Johansen scheme， better describes soil thermal conductivity during SFT.The thermal-hydro-deformation interaction thermal conductivity scheme comprehensively describes the water-heat coupling and frost heave impacts， resulting in more accurate simulation of characteristics of soil thermal conductivity in the drastic phase transition.（2） Supercooled water parameterization scheme can depict the existence of liquid water below 0 °C in soil.Variable freezing threshold parameterization depicts that water phase transition to ice happens below 0 °C.Taking account of the impedance of soil ice to liquid water infiltration improves model performance in simulating the hydrological process in frozen soil.（3） The water-heat coupled scheme is proposed to capture the synergistic changes of both thermal and hydraulic processes in soil， especially the interaction between water and heat.These schemes describe complex physical mechanisms during SFT in detail， and therefore can reduce model biases in simulating the transfer and vertical distribution of heat and water in soil.（4） Most numerical models with an isothermal framework assume that phase change of soil water/ice occurs in the middle of each soil layer and the entire model layer is either frozen or thawed， resulting in serious misestimates of the freeze-thaw depth in soil.To solve this problem， the freeze-thaw front parameterization scheme is developed and incorporated into models.Despite great progress in simulating SFT， there are still some deficiencies.Saline soil lowers freezing point of soil water， but this has not been considered in most current numerical models； although the impact of SOM on soil thermal and hydraulic conductivities has been taken into account， the content of SOM and its vertical distribution is not realistically associated with the growth of vegetation roots； the entire soil depth is not sufficient deep and the assumption of zero heat flux through bottom of soil in numerical models is not the case in the reality.Therefore developments of parameterization schemes to simulate the transfer and distribution of soil salt， to depict the root growth and vertical distribution of SOM， to take account of the influence of deep soil layers and real bottom boundary conditions are among the possible improvements in the future land models to improve the simulation of SFT.