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Panspermia is the idea that life migrates naturally through space. Although an old idea, there has been much recent theoretical and experimental work developing the idea in recent years. In this review, this progress is considered and placed in context. Ideas concerning Panspermia now include mathematical treatments of the likelihood of transfer of life from Mars to Earth, the possibility of life transferring between the natural satellites of an outer planet such as Jupiter, and mathematical treatments and models of life migrating out of a Solar System. Not all predictions of the likelihood of successful Panspermia are positive, and some are contradictory. At present, Panspermia can neither be proved nor disproved. Nevertheless, Panspermia is an intellectual idea which holds strong attraction. However, at the heart of Panspermia is a still un-resolved mystery: in order to migrate, life has to start somewhere, and we still cannot tackle that moment of origin.