The Structural Maintenance of Chromosomes (SMC) protein complexes are DNA-binding molecular machines required to shape chromosomes into functional units and to safeguard the genome through cell division. These ring-shaped multi-subunit protein complexes, which are present in all kingdoms of life, achieve this by organizing chromosomes in three-dimensional space. Mechanistically, the SMC complexes hydrolyze ATP to either stably entrap DNA molecules within their lumen, or rapidly reel DNA into large loops, which allow them to link two stretches of DNA in cis or trans. In this chapter, the canonical structure of the SMC complexes is first introduced, followed by a description of the composition and general functions of the main types of eukaryotic and prokaryotic SMC complexes. Thereafter, the current model for how SMC complexes perform in vitro DNA loop extrusion is presented. Lastly, chromosome loop formation by SMC complexes is introduced, and how the DNA loop extrusion mechanism contributes to chromosome looping by SMC complexes in cells is discussed.