Eye creams marketed for anti-aging typically contain the same retinoids, peptides, and antioxidants as face products — at lower concentrations, in richer vehicles, at higher prices. The 'eye-specific' premium is mostly marketing.
Where eye-specific products do earn their place
Retinol formulated for under-eye sensitivity (lower concentration, richer base reduces irritation). Caffeine for morning puffiness (real but temporary effect). Vitamin K for blue/purple shadowing (limited but real evidence).
What works as well as 'eye creams'
Your face moisturiser (if fragrance-free, low-irritation) applied gently to under-eye area. A small dab of face retinol (at lower frequency) for crow's feet. Daily SPF extending under-eye. None of these requires a dedicated eye product.
Most users could replace their eye cream with their face moisturiser plus sunscreen and lose nothing. Spend the saved money on better sunscreen.