Abstract Just as we must see to the health of individual people when we venture permanently beyond Earth, we will have to see to the health of our populations—the gene pool, which in practical terms is composed of groups of families. In popular culture this often immediately brings up the spectre of ‘genetic screening’ for space settlement, as depicted in the 1990 film ‘Gatacca’. In that film a draconian genetic-screening programme sought to establish a ‘super race’ of spacefarers. While the film had useful messages about genetic screening generally, it was entirely wrong about what will make for successful populations of people beyond Earth; it is genetic diversity, not uniformity, that is most likely to make for success beyond Earth, as new selective environments and pressures are encountered, and in fact themselves change through time in ways that we will only learn when we experience them. How to maintain genetic health, diversity, then, in the project of space settlement? This chapter tackles this fascinating question by evaluating the well-known drivers of population genetic change, namely mutation, migration, selection and drift. We will also explore important questions of humanity’s Minimum Viable Population, a figure often of interest to space planners but one I suggest is a useful guide only for early populations which I recommend to grow rapidly as insurance against catastrophe, to which small populations are most vulnerable. I also present several formulae useful to estimation of populations of space settlers in various circumstances and mention other current models. Finally, I discuss genetic screening and testing in relation to the issue of the genetic constitution of space-settling populations, and make recommendations regarding extraterrestrial human population sizes based on a broad review of human and other population phenomena and the lessons of several billion years of Earth life evolution; these supply important lessons in the fossil and genetic records. This chapter updates and expands upon work I first published in Acta Astronautica, in 2014, regarding viable populations for interstellar voyaging. While that paper was interesting and useful, the fuller expression of its theory and application are found in this chapter.