In an attempt to describe the morphofunctional consequences of uni- and bilateral aplasia of the common carotid artery (CCA), which is usually a vascular source of the external carotid (ECA) and internal carotid (ICA) arteries, we investigated online databases of anatomical and clinical papers published from the 18th century to the present day. We found 87 recorded cases of uni- and bilateral CCA aplasia in subjects from the first hours to the eighth decade of life, which had been discovered in 14 (known) countries. Four crucial parameters were described: the embryology of the carotid arteries, morphophysiology of the carotid arteries, CCA aplasia, and unilateral versus bilateral CCA aplasia, including history, general data, diagnosing, vascular sources, caliber, course of the separated ECA and ICA, associated vascular variants, and pathological disorders. To complete the knowledge of the morphofunctional consequences of the absence of some artery of the carotid system, and risking the possibility of repeating some words, as “carotid artery”, or “carotid aplasia” and the headings from our previous article about bilateral ICA absence, this review is the first in the literature that recorded all cases of the CCA aplasia published and/or cited for the past 233 years. Main characteristic of the CCA absence is its association with 21 different diseases, among which the aneurysms were in 13.69% of cases, and 17.80% of cases were without pathology.