Did Early Christians Believe in Reincarnation?

Many people in the modern western world view reincarnation as a belief predominately from eastern religions - especially buddhism and hinduism.

Believe it or not, reincarnation was also a theological concept for some early Christians! How does what early Christians taught about reincarnation differ from what we understand it to be?

Was it a common idea, or did those who espoused it receive pushback and censorship from their fellow Christians?

Why isn't reincarnation still a widely held view in Christian circles?