The azygos vein is a vessel that drains deoxygenated blood from the posterior wall of the thorax and upper abdomen into the superior vena cava. It can vary morphologically in both adults and fetuses in origin, termination, diameter, course, and tributaries, especially the hemiazygos vein and accessory hemiazygos vein, which, together with the azygos vein, form the azygos venous system. The main aim of this review is to summarize the current state of knowledge regarding the azygos vein. Another aim is to present the morphological variations of the azygos vein and their clinical significance. This information may be useful to clinicians, especially surgeons. This review also provides an overview of the embryological development of the azygos venous system and the consequences of its developmental errors, as well as their relationship to certain clinical cases and pathologies.