A safe design of hydraulic structures depends on reliable estimations of the scour generated by the interaction between flow, structure, and bed sediments. Non-cohesive and cohesive soils are characterized by very different scour processes. Consequently, the behavior of the two soil types under scour has usually been studied separately. More specifically, cohesive soils are subjected to significant interparticle forces, which affect the properties of the material, resulting in different erosion mechanisms. Because of the complexity of the problem, erosion processes have been mainly investigated experimentally, resulting in a variety of case-dependent predicting equations. Recent theoretical advancements contributed to clarify the physics of scour in granular materials, paving the way to the development of general tools for its assessment. Nevertheless, a systematic characterization of local erosion in different types of soil is still lacking. The aim of this paper is to present an updated summary of current knowledge on scour caused by circular jets for cohesive and non-cohesive soils, highlighting differences and similarities of the scour phenomenon. In so doing, we also point out the still-challenging aspects and the future lines of research.