To ensure long-term survival of humans and Earth life generally, strategies need to be in place to recolonize Earth after global catastrophes and to colonize exoplanets. In one strategy of space colonization, the physical barriers erected by time and space are circumvented by sending cryopreserved human and animal embryos to exoplanets rather than adult crews. There the embryos would be developed to neonates in artificial uterus (AU) systems. A similar strategy could also be used to repopulate Earth after human extinction events. In this paper, we review the status and future prospects of these embryonic survival strategies. A critical requirement in each scenario is an AU system for complete ectogenesis, i.e. complete development of embryos to neonates outside the natural womb. While such systems do not yet exist, they may soon be developed to afford clinical assistance to infertile women and reproductive choices to prospective parents. In human survival schemes, AU systems would likely first be used to extend conventional survival missions (e.g. subterranean bunkers) by replacing some adult crew members with cryopreserved embryos. For major mass extinctions and all far future events, adult crews would be entirely replaced by embryos and androids. The most advanced missions would feature orbiting embryo spacecraft for Earth recolonization and analogous interstellar spacecraft for colonizing exoplanets. We conclude that an advanced civilization using such an integrated, embryonic approach could eventually colonize distant parts of its home galaxy and potentially the wider universe.