Find out what is casting the shadow
Dark under-eye circles have several different causes, and the right treatment depends entirely on which one is yours. Pigmentation shows as genuine brown discoloration in the skin. Vascular circles look blue or purple, from blood vessels showing through skin that is naturally thin under the eye. Structural shadowing is not color at all, it is a hollow under the eye socket casting a shadow.
You can tell them apart quickly. Gently stretch the skin sideways: pigment moves with the skin, vascular color fades, a structural shadow barely changes. Once you know which you are dealing with, the shortlist gets much shorter. Brightening ingredients help pigment, caffeine and vitamin K help vascular circles, and hollowing responds to filler rather than cream. The reviews below cover the eye creams worth trying for the first two.