As a Facial Plastic Surgeon, I have been asked to correct under eye circles more times than I can remember… Not all circles are the same, however, and unfortunately there is no single treatment that can help all circles. So to best answer your question, let's break it down by causes.
1. Under eye circles caused by skin pigmentation
Can be genetic, and may present relatively early in life. They can get worse as the lower eyelid complex looses fat and skin becomes loose and contracted. Thereby leaving the melanin in the dermis (pigment in skin) contracted, more concentrated, and thus appearing darker.
Treatment for this includes skin bleaches such as hydroquinone, sometimes in combination with retinol (Retin-A), or chemical peels.
2. Under eye circles caused by volume loss
This is a thinning of the skin and loss of fat in the area that leaves the inferior orbital rim (lower portion of the eye socket bone) in a shadow - the skin may be contracted, but the pigmentantion in these cases is not the only issue. Treatment for this is based solely on augmentation of the “tear trough” and infra-orbital rim area. This is done using fillers like hyaluronic acid (Restylane), or fat, and has great results in my practice (www.noseandface.com - click on non-surgical treatments or fox news links.) This refers to the Thirties Eyelift that is a quick in office treatment for the lower eyelid area that looks prematurely aged in the condition above.
3. Under eye circles caused by thinning of the skin only
This is related to the unique anatomy of the area which leaves the thin layer of skin over the muscles surrounding the eye with no fat layer in between -- the color of blood flow in the muscle shines through the skin. This is tough to treat, but likely is the target of almost all of the under-eye topical preparations on the market. I have heard success stories and disappointments with almost every single one of these products, and don’t support any particular one, but I do recommend starting one and continuing with it for several months before giving up. Then if it does not work, a different product may be applied. I generally recommend Teamine, or Hylexin, and it probably makes no difference which one you use -- you just may get lucky with one of them.
4. Other causes include allergy
So called allergic shiners also result from the unique anatomy of the area and its tendency to swell more than other areas of skin in the face. Allergy treatments such as antihistamines or avoidance of allergens may help with this.