The purpose of the present review is to report the anatomic and the clinical-surgical aspects involved in the celiac trunk compression syndrome by the median arcuate ligament of the diaphragm, reviewing the major findings of the syndrome in the anatomic field during dissection of cadavers, followed by clinical-surgical findings of stenosis of the celiac trunk, the relationship of this stenosis with the patient's symptoms and healing after decompression of that artery; invasive and non-invasive methods used to diagnose compression; the stenotic effect of physiologic mechanisms of the median arcuate ligament, aorta and celiac trunk displacement during respiration; anatomy of the aortic channel and celiac plexus; the median arcuate ligament and the celiac plexus as constrict agents; skeletopy of the celiac trunk, the median arcuate ligament and predisposition to syndrome; association of the syndrome with morphological and metabolic aspects