Soil compaction caused by agricultural vehicles is a global problem affecting a considerable proportion of all arable land and causing tremendous costs to farmers and society. Soil compaction reduces soil porosity and modifies pore geometry, thereby adversely affecting key soil ecological, hydrological and agronomic functions. This chapter provides an overview of current knowledge on stress propagation, soil compressive behaviour, impacts of soil compaction on soil properties and functions and recovery of soil structure after compaction, and discusses the costs of soil compaction. We provide an overview of non-destructive measurement techniques and approaches for improving description and quantification of soil compaction at spatial scales from the soil pore to the field. Finally, we discuss sensor systems for on-the-go mapping of soil compaction and provide a perspective for future development of sensor fusions for soil compaction identification and mapping.