Treat under-eye bags. The only good treatment for under-eye bags is surgery called a lower lid blepharoplasty. Some believe that certain topical creams or serum help, but surgery is the only definitive way to look better. This is generally not a difficult procedure and can make an enormous difference.
Need an examination. There are a number of different problems that can cause "bags" under the eyes. It may be swelling or prominence of the eyelid fat. It might be due to changes in the eyelid skin. It might be due to thyroid or other hormone problems. You should see an eye doctor or surgeon who does eyelid surgery to get an accurate diagnosis and appropriate treatment.
Surgery. Bags under eyes are due to genetic disposition for the fat around the eye to slip forward and create bags. For large bags, surgery is the only solution. For small bags , different methods of skin tightening ( radiofrequency, laser resurfacing etc.) can be used to reduce the appearence of the bags.