The part of the human body that has no blood is the cornea, the transparent outer layer of the eye.
The cornea's lack of blood vessels is crucial for its function. It needs to be transparent to allow light to pass through and reach the retina. Blood vessels would block light and obscure vision.
Instead of relying on blood for oxygen and nutrients, the cornea gets these from the surrounding aqueous humor, a fluid that fills the front chamber of the eye.
The cornea is a fascinating example of how the human body adapts to its needs.