The COG complex is a cytosolic heteromeric Golgi complex constituted of 8 subunits (Cog1 to Cog8) and involved in retrograde vesicular Golgi trafficking. The involvement of this complex in glycosylation and more specifically in Golgi glycosyltransferases localization has been highlighted with the discovery of COG subunit deficiencies leading to CDG (Congenital Disorders of Glycosylation), a group of inherited disorders of glycosylation. To date, many COG deficient CDG patients have been discovered and this article reviews the birth and rise of this group of defects. The architecture of the COG complex and its cellular functions in Golgi trafficking and Golgi glycosylation are discussed.