The external carotid artery (ECA) supplies blood to the face, scalp, and neck, branching into various arteries like the superior thyroid, lingual, and facial arteries. It is bifurcated from the common carotid artery, which also gives rise to the internal carotid artery that supplies the brain and eyes. Surgical procedures for managing conditions related to the ECA, including endarterectomy and ligation, require careful evaluation due to associated risks.