Description: The white part of the eyeball is called the sclera (say: sklair-uh). The sclera is made of a tough material and has the important job of covering most of the eyeball. Think of the sclera as your eyeball's outer coat. Look very closely at the white of the eye, and you'll see lines that look like tiny pink threads. These are blood vessels, the tiny tubes that deliver blood, to the sclera.