The conserved oligomeric Golgi (COG) complex, a multisubunit tethering complex of the CATCHR (complexes associated with tethering containing helical rods) family, controls membrane trafficking and ensures Golgi homeostasis by orchestrating retrograde vesicle targeting within the Golgi. In humans, COG defects lead to severe multisystemic diseases known as COG‐congenital disorders of glycosylation (COG‐CDG). The COG complex both physically and functionally interacts with all classes of molecules maintaining intra‐Golgi trafficking, namely SNAREs, SNARE‐interacting proteins, Rabs, coiled‐coil tethers, and vesicular coats. Here, we review our current knowledge of COG‐related trafficking and glycosylation defects in humans and model organisms, and analyze possible scenarios for the molecular mechanism of the COG orchestrated vesicle targeting.