Background and Objectives: The carotid bifurcation (CB) is presented in most anatomy textbooks as having a unique location at the upper margin of the thyroid cartilage. Although a number of case reports have provided evidence of the possibility of carotid artery location either lateral or medial to the greater hyoid horn, these reports have not established specific anatomic possibilities and prevalences. Materials and Methods: We retrospectively analysed a batch of 147 CT angiograms for 12 types of carotid–hyoid relationships and classified the bilateral combination possibilities of these types. Results: In 168/294 sides there were no carotid–hyoid relationships. Type I, external carotid artery (ECA) medial to the greater horn of the hyoid bone (GHHB), was observed in 0.34%; type II, internal carotid artery (ICA) medial to GHHB, in 0.34%; type III, ICA and ECA medial to GHHB, in 1.02%; type IV, common carotid artery (CCA) medial to GHHB, in 1.02%; type V, CB medial to GHHB, in 0.34%; type VI, ECA lateral to GHHB, in 20.41%; type VII, ICA lateral to GHHB, was not recorded; type VIII, ECA and ICA lateral to GHHB, in 3.74%; type IX, CCA lateral to GHHB, in 8.5%; type X, CB lateral to GHHB, in 6.46%; type XI, ECA lateral and ICA medial to GHHB, in 0.34%; and type XII, ICA lateral and ECA medial to GHHB, in 0.34%. Bilateral symmetry was found in 70.74% of cases, including the null types without carotid–hyoid relationships as well as types IV, VI, VIII, IX, and X. There was a highly significant association between the left and right variants of the carotid–hyoid relationship. Conclusions: Mechanical compression of the hyoid bone on the carotid arteries has various undesirable effects on the ICA and cerebral circulation. Underlying these are several variational anatomical patterns of carotid–hyoid relationships, which can be accurately documented on CT angiograms. A case-by-case anatomical study is better than assuming the carotid anatomy learned from textbooks.