Rapid advancements in technology, particularly in soil tools and agricultural machinery, have led to the proliferation of mechanized agriculture. The interaction between such tools/machines and soil is a complex, dynamic process. The modeling of this interactive process is essential for reducing energy requirements, excessive soil pulverization, and soil compaction, thereby leading to sustainable crop production. Traditional methods that rely on simplistic physics-based models are not often the best approach. Computational intelligence-based approaches are an attractive alternative to traditional methods. These methods are highly versatile, can handle various forms of data, and are adaptive in nature. Recent years have witnessed a surge in adapting such methods in all domains of engineering, including agriculture. These applications leverage not only classical computational intelligence methods, but also emergent ones, such as deep learning. Although classical methods have routinely been applied to the soil–machine interaction studies, the field is yet to harness the more recent developments in computational intelligence. The purpose of this review article is twofold. Firstly, it provides an in-depth description of classical computational intelligence methods, including their underlying theoretical basis, along with a survey of their use in soil–machine interaction research. Hence, it serves as a concise and systematic reference for practicing engineers as well as researchers in this field. Next, this article provides an outline of various emergent methods in computational intelligence, with the aim of introducing state-of-the-art methods to the interested reader and motivating their application in soil–machine interaction research.