Elijah doesn't have his own book in the Bible, though think he probably deserved one. His story starts in 1 Kings at verse 17 and continues into 2 Kings.
Elisha, who is basically Robin to Elijah's Batman, apears in 1 Kings 19:19.
In 2 Kings verse 2, God takes Elijah up to Heaven in a whirlwind. Elisha witnesses this, then takes over the mission. He dies naturally in 2 Kings 13:20.