There is a contradiction at the heart of our current understanding of mobility patterns. On one hand, a highly influential stream of literature driven by analyses of massive empirical datasets finds that human movements show no evidence of characteristic spatial scales. There, human mobility is described as scale-free. On the other hand, in geography, the concept of scale, referring to meaningful levels of description from individual buildings through neighborhoods, cities, regions, and countries, is central. Here, we resolve this apparent paradox by showing that human mobility does indeed contain meaningful scales, corresponding to spatial containers restricting mobility behavior. The scale-free results arise from aggregating displacements across containers. We present a simple model, which given a person’s trajectory, infers their neighborhoods, cities and so on. We find that the containers characterizing the trajectories of more than 700,000 individuals worldwide do indeed have typical sizes. We show that our description improves on the state-of-the-art in modeling, and allows us to better understand effects due to socio-demographic differences and the built environment. Additional resources: https://observablehq.com/@lauale/a-model-for-generating-multiscale-mobility-traces https://observablehq.com/@ulfaslak/a-visual-exploration-of-how-a-power-law-can-emerge-from-aggre https://github.com/lalessan/scales_human_mobility https://github.com/ulfaslak/infostop