The tear trough is a name for the arc of depressed tissue that starts between the eye and the nose and often fades as it moves toward the outer rim of the eye. It is distinct from, but often accompanies, "bags" under the eyes. Bags are puffy regions either on the lower lid or below it, which may or may not be dark in color. Depending on whether you have one, the other or both, you will receive different treatment.
Lower lid blepharoplasty (eyelid surgery) has long been the recommended treatment for puffy eyelids and bags under the eyes. The removal of excess fat from the lids can restore their youthful appearance. It was the second most popular cosmetic surgery procedure for men in 2008, and in the top five for women.
The tear trough is significantly different. Although some may experience significant hollowness around the eyes as a result of sinking mid face tissues, for the majority of people the tear trough is the result of lost facial volume, and doesn't respond to surgical treatment. Instead, facial filler injections are the best course of treatment for the phenomenon. Those with puffy lower lids can sometimes use them as donor regions for fat that is used to fill the trough. For others, fat transplantation from other areas is an option, as are other injectable facial fillers.