Many people think that concealers are
    the same as foundations and, to some degree, that's true. In a way, you can
    look at concealers like concentrated foundations but the fact of the matter is,
    concealers have a very specific role to play and they have to perform in
    concert with foundations over which they are applied. And that means matching
    colors. In no event should you ever consider going more than one shade lighter
    or darker that you skin tone or foundation tone, especially when you're trying
    to hide large problem areas like under the eye circles

That being said, concealers work well
    to hide circles under the eyes. Like all concealers, use it sparingly as it
    tends to "cake-up" and choose a pink- or peach-based concealer. Yellow-bases
    tend to combine with the dark colors to heighten the effect. For the areas of
    the face where light generally hits, a yellow-based concealer is typically
    used. And, if you have fair skin, look for a concealer with subtle pink tones a
    shade darker than your skin. If you have dark skin, go for a copper-toned
    concealer a shade or two lighter than your skin.

Here is an overview of how the various color choices are used by the studio industry:

Matte White: Lightens Darker Foundations, Use to Enhance Features and Highlight Cheekbones, Use as a Spot Treatment for Blemishes, Use as Goth Makeup.

Yellow: Hides Undereye Circles, Dark Spots and Purple Blotches, Adds Warmer Tones when Mixed with Cool Toned Foundations. Balances out Orange/Red tones in Light Complexions.

Mint (Green): Covers Redness, Acne and Rosacea. Also used after laser and chemical peels to cover Redness. Use as Goth Makeup.

Lavender: Hides Bruises and is used to Cover the after effects of Plastic Surgery. Also, Neutralizes Yellow Tones and Gives Sallow Complexions a Healthy Glow.
 
Mauve: Used to Even out Blue and Black Tones found in Bruises, Veins and Under Eye Circles.

Peach: Hides Blue Undereye Circles. Also used to Liven up Overall Skin Tone and Add a Healthy Glow. Balances out Slight Discolorations.

The biggest issue with concealers after correct color selection
    is application. Studio Direct Cosmetics has a great selection of concealers with just
    the right colors needed for the camera. Where ever you use concealer, use as little as
    possible and then spread it out with your fingers or a concealer brush. If it's
    under the eyes, start at the upper, inner corner of your eye and blend down and
    under. Blend until product is completely absorbed. If it's for scars or
    birthmarks, 1) use concealer only if the wound is healed to a scar and 2)
    if the birthmark or scar is extremely dark, use white first to lighten the area
    and then the concealer color closest to your skin tone over the white. In both
    cases, use a professional sponge to apply. Finally, on Rosacea or other problem
    areas, apply with a sponge and only to the areas needing coverage.