Abstract: Impact behavior is a ubiquitous phenomenon in multibody systems. The contact force model is a pivotal tool to predict the contact characteristics of multibody systems. At present, there are two kinds of contact models used for calculating impact behaviors: the static elastoplastic contact force model and the continuous contact force models with energy dissipation. There are many similarities and discrepancies among them in the impact dynamics of multibody systems. This review starts with the introduction of development history of these two kinds of contact models followed by their development progress and background illustrated in detail. Firstly, whether the initial impact velocity is contained in the denominator of damping term severs as a criterion to classify the continuous contact force model as two types of models that are the contact force model with hysteresis damping factor and the other one with viscous damping factor. The relationship between the power exponent and Hertz contact stiffness is analyzed. The problems in calculating the elastic-plastic contact collision behavior by using the existing continuous contact force models are discussed. Secondly, the static elastoplastic contact force models with the continuous transition between the pure elastic and full plastic are introduced, and its characteristic is illustrated when calculating the elastoplastic collision events. The coefficient of restitution acts as the bridge to connect the static elastoplastic contact model and dynamic dashpot model as a complete system. In order to sidestep the error from the Hertz contact stiffness in calculating the elastoplastic impact behavior, a new viscous damping factor is derived by means of the linear elastoplastic contact stiffness based on energy conservation. The intrinsic connection between the static elastoplastic model and the dashpot model is explored, which proves that the artificial damping describing energy dissipation is equivalent to the one generated by the discrepancy between the loading and unloading paths. In order to avoid the numerical singularity caused by the initial impact velocity in the denominator of damping when calculating the dynamic performance of granular matter, a continuous contact force model with viscous damping is obtained by solving a linear single degree of freedom underdamped vibration system. One-dimension chain is taken as the numerical example to validate that the new dashpot model is more accurate than the one used in the EDEM software. Finally, the current research status of impact dynamics of multibody systems is reviewed, and the development trend and future challenges of contact force models are briefly summarized.