Many monsters were created on the Sixth Day, some destroyed during the Flood, some still here. Re'em is described as a giant even among these strange animals. At any given time, only two exist, one male and one female, because had more of them existed, the world could not support them.
The word may be related to the Akkadian "rimu", which means, "wild ox", which would add credence to the idea that it was originally the aurochs. 
No one is certain what Re'em looks like. The sources describe him as fierce, fast, and indomitable. Scholars argue about the number of his horns, some say he has one, like a unicorn or a rhinoceros. Some say two, and he could be related to the giant Aurochs, a species of a wild ox that became extinct during the sixteenth century. On the other hand, he may be a purely mythological creature, based on the reliefs of the huge Egyptian beasts that were unquestionably familiar to the Jews.
Re'ems live at the opposite ends of the earth, one in the east, the other in the west, and for seventy years never see each other until the day of their mating season. Finally they meet, mate once, and then the female kills the male.
The female becomes pregnant, and her pregnancy lasts for twelve years. During the last year she cannot walk and survives only because her saliva waters the earth around her sufficiently to produce enough vegetation for her support. Instead of giving birth, her stomach bursts open and she dies instantly. However, twins are born, one male and one female. They get up immediately and wander away, one to the east, one to the west.
The beast is mentioned nine times in the Bible (Job 39:9,10, Deuteronomy 33:17, Numbers 23:22 and 24:8; Psalm 22:21, 29:6 and 92:10; and Isaiah 34:7).
King David had an encounter with a Re'em. When David was still a simple shepherd, he saw a sleeping Re'em and thought it was a mountain. He started climbing it, and the Re'em awoke and lifted David on his gigantic horns. David vowed that if God saved his life, he would build Him a temple, a building as high as the Re'em himself. God heard him and sent a lion. As the lion is the king of the beasts, the Re'em bowed to him by prostrating himself on the ground, and David could descend from the horns. Then God sent a deer, and the lion started chasing her. So David was saved from both the lion and the Re'em.
Theory about existence
Translated to unicorn in the King James version of the Bible, it is translated as "wild ox" in the NASB. Also speculated to refer to the Arabian Oryx or the extinct aurochs. Some Creationists believe it to be a ceratopsid.
In the Harry Potter universe of JK Rowling, Re'em are described as "extremely rare giant oxen with golden hides," whose blood bestows great strength on anyone who drinks it.