Many Buddhists understand the Round of birth-and-death quite literally as a process of reincarnation, wherein the karma which shapes the individual does so again and again in life after life until, through insight and awakening, it is laid to rest. But in Zen, and in other schools of the Mahayana, it is often taken in a more figurative way, as that the process of rebirth is from moment to moment, so that one is being reborn so long as one identifies himself with a continuing ego which reincarnates itself afresh at each moment of time.
