Puffiness around the Eyes
If you have puffy skin around the eyes, use an eye cream that contains caffeine which allows a temporary de-puffing by constricting blood vessels in the area. For example, try SkinCeuticals AOX+ Eye Gel OR Exuviance DePuffing Eye Serum
Dark Circles under Eyes
For dark circles
go for an eye product which contains ingredients such as vitamin C, licorice, Kojic acid, Chromabright or niacinamide which inhibit melanin production. For example, try Jan Marini Luminate Eye Gel
Please bear in mind that dark circles are very difficult to treat. It also has a lot to do with your diet and lifestyle.
Look for eye products that contain Retinol (Vitamin A), Vitamin C, Peptides & Growth factors.
The more that any of the anti-ageing ingredients mentioned above are included in your eye creams the better.
If the eye area is sagging/baggy I am afraid an eye cream cannot help. Only surgery will help remove that excess skin.
Dry & Crepey Skin Around The Eye Area
If the skin around your eyes is drier, then you need hydrating ingredients like HA (Hyaluronic Acid). HA is great as it is a hydrating ingredient but not too heavy. Obviously if you need something more hydrating, then go for an emollient type of eye cream like a balm or a product that contains vitamin E. Be careful not to go too heavy if you don't need to as it may cause milia around the eye area.
Make sure you're using your eye cream correctly
You do not need to use too much - just a pea sized amount will suffice. Apply using your ring finger for a light touch. Dab small dots under and around your eyes and on the brow bone. Don't rub or stretch or pull the skin.
It's vital that you protect your skin daily against the sun. This also applies to the skin around the eyes. The problems of wrinkles, dark circles, etc. will only get worse if you go out without sun protection. Use either an eye SPF sunscreen or a mineral SPF sunscreen or make sure that your concealer is a minimum of SPF30 or higher. And lastly don't forget to wear sunglasses.