Head veins. Historical illustration of the veins (red) and muscles (blue and white) of the head and neck. Veins drain blood from the body towards the heart. Here, they branch out across the scalp and face, bringing blood back to a major vein, the external jugular vein of the right-hand side of the neck. This external branch of the jugular vein passes over the sternomastoid muscle (running down diagonally from the ear towards the chest). The internal jugular vein branches off near the jaw, passing behind the sternomastoid muscle. This arrangement is repeated on the left-hand side of the head. The head arteries are deeper in the head than the veins seen here.