While it is unclear how molecules move between adjacent Golgi cisternae, it is apparent that the molecules move from cis- cisterna, the entry face, to the trans- cisterna, the exit face. Experiments initially suggested vesicles that bud from one cisterna and fuse with the next cisterna to transport proteins between the cisternae. This vesicular transport model describes the Golgi apparatus as a relatively static structure with a unique enzyme composition in each cisterna. Molecules are transported in vesicles through the cisternae in a specific order, determining the modifications made to the substrates.

An experiment that used collagen rods in fibroblasts contradicted the vesicular transport model as collagens are too large to fit in the classical vesicles. This led to an alternative hypothesis, the Cisternal maturation model. According to this model, the Golgi apparatus is a dynamic structure where the cisternae move through the Golgi stack. The vesicles that arrive from the ER fuse with one another to become a vesicular tubular cluster that matures to become a cis-cisterna. Then, the cis-cisterna progressively matures to become a medial cisterna and subsequently trans-cisterna. As a new cis-cisterna continually forms and migrates, its enzyme composition changes. COPI-coated vesicles budding out of the mature cisternae carry the enzymes back to the newer cisterna, where they are functional. Thus, a newly formed cis-cisterna would receive resident enzymes primarily from the cisterna just ahead of it.

The two models described are not mutually exclusive. Experiments suggest that a stable core of long-lasting cisternae might exist in the center of each Golgi cisterna, and some vesicle-bound cargo moves forward rapidly. In contrast, other cargo moves forward more slowly, leading to the renewal of the Golgi apparatus through cisternal maturation. Thus, Golgi transport may involve a combination of mechanisms described in the two models.