Population matters. Demographic patterns are both a cause and a consequence of human behaviour in other important domains, such as subsistence, cooperation, politics and culture. Demographers interested in contemporary and recent historical populations have rich data at their fingertips; the importance of demography means many interested parties have gathered demographic data, much of which is now readily available for all to explore. Those interested in the demography of the distant past are not so fortunate, given the lack of written records. Nevertheless, the emergence in recent years of a new interest in the demography of ancient populations has seen the development of a range of new methods for piecing together archaeological, skeletal and DNA evidence to reconstruct past population patterns. These efforts have found evidence in support of the view that the relatively low long-term population growth rates of prehistoric human populations, albeit ultimately conditioned by carrying capacities, may have been owing to 'boom-bust' cycles at the regional level; rapid population growth, followed by population decline. In fact, this archaeological research may have come to the same conclusion as some contemporary demographers: that demography can be remarkably hard to predict, at least in the short term. It also fits with evidence from biology that primates, and particularly humans, may be adapted to environmental variability, leading to associated demographic stochasticity. This evidence of the fluctuating nature of human demographic patterns may be of considerable significance in understanding our species' evolution, and of understanding what our species future demographic trajectories might be. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.