Spatial cognition is fundamental to our species. One might therefore expect that spatial communication systems would have evolved to make common distinctions. However, many have argued that spatial communication systems exhibit considerable cross-linguistic diversity, challenging the view that space structures language. We review recent work on spatial communication that merits revisiting the relationship between language and space. We provide a framework that places action as the driver of spatial communication systems across languages, in which spatial demonstratives - the earliest spatial terms - play a fundamental role in honing attention and theory of mind capacities that are crucial for language and cognition more broadly. We discuss how demonstratives emerged early in language evolution to serve a combination of spatial, social, and functional needs.