Human evolutionary ecology stands to benefit by integrating theory and methods developed in movement ecology, and in turn, to make contributions to the broader field of movement ecology by leveraging our species' distinct attributes. In this paper, we review data and evolutionary models suggesting that major changes in socio-spatial behaviour accompanied the evolution of language. To illustrate and explore these issues, we present a comparison of GPS measures of the socio-spatial behaviour of Hadza hunter-gatherers of northern Tanzania to those of olive baboons (Papio anubis), a comparatively small-brained primate that is also savanna-adapted. While standard spatial metrics show modest differences, measures of spatial diversity, landscape exploration and spatiotemporal displacement between individuals differ markedly. Groups of Hadza foragers rapidly accumulate a vast, diverse knowledge pool about places and things over the horizon, contrasting with the baboon's narrower and more homogeneous pool of ecological information. The larger and more complex socio-spatial world illustrated by the Hadza is one where heightened cognitive abilities for spatial and episodic memory, navigation, perspective taking and communication about things beyond the here and now all have clear value.This article is part of the theme issue 'The spatial-social interface: a theoretical and empirical integration'.