There are two areas to be considered, the upper eyelid and brow area, and the lower eyelid and cheek area.
For the upper eyelids, an upper eyelid blepharoplasty would be a good start. Techniques vary widely, and we prefer a fat preservation technique rather than an aggressive approach to the fat. We also prefer a conservative approach to the skin rather than an aggressive removal of skin. There is also some drooping of the lateral brow which can be separately addressed through a lateral browlift (see book chapter referenced below). Every surgeon has their signature style for this procedure, so look carefully at the before and after pictures to see which style suits you best.
For the lower eyelids, there appears to be several issues with your eyes. First, they are prominent. The lower eyelid is sagging away from the eyeball, causing the corners of the eye to go down. Removal of any skin at all from the lower eyelid will result in a rounding or further pulling down of the corner of the eye. This will occur with certainty unless the corner of the eye is supported. We prefer a USIC cheeklift (ultrashort incision cheeklift), also referenced below. This allows support of the corner of the eye and enables safe tightening of the lower eyelid skin without any disturbance of the orbital septum, the very dangerous layer connecting the lower eyelid with the bone. In your case, there also appears to be extra fat. This can either be redistributed or reduced through a transconjunctival incision through the lower eyelid, again avoiding the orbital septum.
Especially in patients with an existing (or postsurgical) alteration of the lower eyelid, support of the lower eyelid is key. This does not just involve a canthopexy, which is inadequate in my opinion as a support technique for most lateral lower eyelid problems. Resurfacing with various lasers will help in changing skin sun damage or fine wrinkles, and is an important adjunctive procedure as well in the right patient.
So you can see we have come a long way from "upper eyelid and lower eyelids" for an eyelid shape problem.