Recent years have seen an increasing amount of work by physicists on topics outside their traditional research domain, including in geography. We explore the scope of this development, place it in a historical context dating back at least to statistical physics in the nineteenth century, and trace the origins of more recent developments to the roots of computational science after the Second World War. Our primary purpose is not historical, however. Instead, we are concerned with understanding what geographers can learn from the many recent contributions by physicists to understanding spatiotemporal systems. Drawing on examples of work in this tradition by physicists, we argue that two apparently different modes of investigation are common: model-driven and data-driven approaches. The former is associated with complexity science, while the latter is more commonly associated with the 'fourth paradigm', more recently known as 'big data'. Both modes share technical strengths, and more importantly a capacity for generalization, which is absent from much work in geography. We argue that although some of this research lacks an appreciation of previous geographical contributions, when assessed critically, it nevertheless brings useful new perspectives, new methods and new ideas to bear on topics central to geography, yet neglected in the discipline. We conclude with some suggestions for how geographers can build on these new approaches, both inside and outside the discipline.