An emerging focus on the geometry of representational structures is advancing a variety of areas in social perception, including social categorization, emotion perception, and trait impressions. Here, we review recent studies adopting a representational geometry approach, and argue that important advances in social perception can be gained by triangulating on the structure of representations via three levels of analysis: neuroimaging, behavioral measures, and computational modeling. Among other uses, this approach permits broad and comprehensive tests of how bottom-up facial features and visual processes as well as top-down social cognitive factors and conceptual processes shape perceptions of social categories, emotion, and personality traits. Although such work is only in its infancy, a focus on corroborating representational geometry across modalities is allowing researchers to use multiple levels of analysis to constrain theoretical models in social perception. This approach holds promise to further our understanding of the multiply determined nature of social perception and its neural basis.