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The mobility of vehicles in off-road environments is critical for many applications. Understanding and predicting the tire-soil interaction is a challenge, especially when the terrain is largely deformable and plastic, and non-linear behavior is expected. This paper presents an overview of the bibliographic references on tires–deformable soil interactions and identifies the gaps present in the literature. The capabilities and challenges of different modeling methods used to assess the traction performance of a vehicle on deformable soil (i.e., analytical, semi-empirical, and numerical are discussed. Also, since the performance of the vehicle highly depends on the soil characteristics, a summary of the different material models used for non-cohesive and cohesive soil and the methods that have been used to characterize the soil is presented. The soil behavior and strength also depend on the water content and permeability along with the soil type. To highlight this, the available works on tire-wet soil interactions are discussed. Lastly, the different tire models and the validation methods that have been used for the soil, tire, and tire-deformable soil interaction are summarized. To conclude, this bibliographic review highlights that there is very limited work in the physics-based study of trafficability in wet soils, in particular in cohesive soil.