What Fillers Are FDA Approved for Use in the Tear Trough / Under Eye Area?

The FDA has not approved any fillers for the tear trough as far as I know. Commonly fillers are approved for the nasolabial folds and doctors use them off -label inthese other areas. I personally prefer restylane for the tear troughs because I think it is more malleable than the others and potentially leads to less risks.

The short answer to your question is "None".  The FDA has not specifically authorized filling in that area.  Using HA fillers in the tear-trough area, however, is commonly performed "off-label".  Using drugs "off-label" is a common practice with many medications.  Once a drug is approved for any purpose, physicians are free to use it as they see fit.  Use of Restylane in the tear-trough is a common treatment and many clinical studies support its use. 

I doubt you will ever see FDA approval for use in the tear-trough area because, as mentioned, the costs associated with doing the FDA designed studies and all of the other associated hassles would be very expensive.  Since physicians and patients are already very accepting of its use there, the FDA approval formalizing its use would likely do little to increase sales and therefore the manufacturers are unlikely to spend the money.