There are few domains as central to cognitive science as language and visual perception. They are typically studied in isolation, yet at some level, they must connect. How? My talk will explore this connection. First, I reveal surprising parallels in how language and vision encode information: Vision, like language, can be compositional. I explore the psychophysics of visual scene composition, finding that the mind builds relational representations (e.g., a vase on a table) in a canonical order. Next, I show that language and vision tap into the same modality-neutral conceptual representations. Using symmetry as a case study, I find a striking correspondence between linguistic and perceptual judgments of the same visual displays. Lastly, I demonstrate how language can offer a window into non-linguistic visuospatial representations, leveraging the unique ways that certain languages encode such properties, particularly Mandarin Chinese. By examining how Mandarin speakers describe novel objects ("daxes") in different visual contexts, I uncover an unexplored influence of spatial relations (a dax in a bowl) on object shape computations. Taken together, my work highlights the representational principles and content shared by language and vision, with implications for how infants acquire language from visual observation.