How can one cease to exist when Jesus and many Bible verses state that hell a real place?

I have a question regarding the topic of hell. How can anyone claim that there isn't a hell when Jesus clearly states that there is? Also, the Bible speaks of fire, screaming, and other horrific descriptions. Please explain how one can cease to exist when the Bible clearly states that people go to hell. In other words, what is the biblical basis for annihilationism ?