What causes puffiness under eyes.

Many things: But most commonly age causes looser tissue which allows orbital fat to prolapse forward.

A few things: There are many possible causes for this: some are allergy, infection, chemical irritation (i.e. from makeup or other facial product being used), some illnesses, heart or blood pressure or kidney problems (especially if there is swelling or puffiness of other parts of the body). I would recommend that you see your doctor to help you figure out the cause.