Spatial language incorporates descriptions of locations, routes, and landscapes, and is used by humans daily. Research has addressed a wide range of aspects of spatial language, including its form; the ways in which it is selected and applied; and cognitive, geometric, and functional factors affecting its use. Furthermore, much work has been done on the automation of spatial language extraction, analysis, interpretation, and generation. To introduce the Special Issue on this broad topic, this paper reviews spatial language research framed by an extension to the well-known semantic triangle, the ‘spatial semantic pyramid’, which represents both human spatial language and relevant computational research. By introducing it, we hope to stimulate discussion about gaps and future directions in this important research field.