Tire-soil interactions are recognized as one of the key scientific topics in the field of off-road vehicle engineering, as such interactions greatly affect the driving, dynamics, and smoothness, of an off-road vehicle. The aforementioned phenomena are quite complicated, which normally involve tire deformations, soil failures, and tire-soil contacts. In recent decades, extensive efforts have been dedicated to developing and using numerical algorithms to reproduce the physical phenomena, as well as to study the interaction mechanism and mode of action between wheels and soils. The purpose of this work is to present a comprehensive and original literature review regarding this aspect. This is achieved by firstly summarizing seven numerical methods for tire-soil interaction simulations, followed by the introduction of material models for numerical modeling of tires and soils. The contact algorithms/models for tire-soil interactions are summarized as well. Finally, the numerical performance of the aforementioned methods on key aspects of tire-soil interaction analyses, i.e., tire traction and deformation as well as soil deformation, flow and failure mechanism, is thoroughly discussed.