The white part of the eye is called the sclera, St. Luke's Cataract & Laser Institute explains. The sclera is made of tissue that is tough and opaque so that it can protect the eye. The optic nerve is attached to the back of the sclera.
St. Luke's Cataract & Laser Institute notes that the sclera tends to yellow as people age. The Ohio Eyecare Specialist website details a surgical procedure called Eye-White that restores the white appearance of the sclera. This out-patient procedure involves modifying or removing the conjunctiva, the thin membrane that covers the sclera. In addition to eliminating the yellow appearance of the sclera, this procedure eliminates any brown pigment in the sclera and the redness that makes eyes appear bloodshot.