Dark under-eye circles can be caused by a combination of different reasons. In darker Mediterranean or Indian complexions, pigmentation is often the cause, while broken capillaries (tiny blood vessels) which leak hemosiderin (iron-containing pigments) make paler skin around the eyes appear purple-brownish. It doesn't help that the skin under your eyes is the thinnest anywhere on your body. Small wonder then, that the little blood vessels beneath show through easily, so that their dark red blood gives the skin a blueish tinge. Most people simply inherit dark under-eye circles, but these can be aggravated by lack of sleep, chronic inflammatory conditions such as eczema or other illnesses. If your bone structure gives you deep under-eye hollows, the lack of light reflection might also appear as dark shadows.
Any underlying illness should, of course, be identified and treated. And, if your dark circles are caused by deep under-eye hollows, this can easily be rectified by certain dermal fillers. But if the main cause is leaky capillaries, a cream containing vitamin K may eventually prove helpful. In the meantime, a good concealer will camouflage the problem instantly.