The surgery to remove the bags under a person's eyes is called blepharoplasty, according to American Society of Plastic Surgeons. This surgery consists of four steps: anesthesia, incision, closing incisions and recovery.
The first step of anesthesia is given as general anesthesia or intravenously, explain American Society of Plastic Surgeons. The next step involves the incision, which is made under the lower lash line. Alternatively, the incision is sometimes made inside the lower eyelid; this is known as a transconjunctival incision. The third step involves closing the incision with removable sutures, skin adhesive or surgical tape. Lastly, the fourth step involves recovery of the swelling and bruising around the eye.