The external iliac artery arises from the bifurcation of the common iliac artery at the level of the L5/S1 intervertebral disc, just anterior to the sacro-iliac joint.  It descends laterally along the medial border of psoas major, along the linear terminalis of the pelvis, enclosed in a thin fascial sheath with its accompanying vein.  It enters the thigh deep to the inguinal ligament midway between the anterior superior iliac spine and the pubic symphysis, where it becomes the femoral artery.

Anteriorly, the peritoneum separates the right external iliac artery from the terminal ilium and possibly appendix and the left external iliac artery from the small intestine and lower descending colon.  The origin of the artery may be crossed by the ureter; in the female the ovarian vessels and in the male the testicular vessels.  The genital branch of the genitofemoral nerve lies on the artery near its lower end, which is also crossed by the ductus deferens or the round ligament of the uterus.  The deep circumflex iliac veins cross all these structures.  The external iliac vein lies partly behind the upper end of the artery but lies medial to the lower part.  Psoas major lies laterally.  

Branches
The external iliac artery gives off two large branches, the inferior epigastric artery and the deep circumflex iliac artery as well as muscular branches to psoas major.