Humans have represented data in many forms for thousands of years, yet the main sensory channel we use to perceive these representations today still remains exclusive to vision. Recent developments now offer us opportunities to perceive data through different levels and combinations of sensory modalities. In this article, we survey the state-of-the-art in data representation that requires more than one sensory channel to fully interpret and understand the data. Drawing on techniques and theories adapted from Thematic Analysis and Prototype Theory, we analysed 154 examples of multisensory data representations to establish a design space along three axes: use of modalities, representation intent and human–data relations. We frame the discussion around presenting how a selection of examples, chosen from the collection, fit into the design space. This not only informs our own research but can also draw the attention of the human–computer interaction and Design Research communities to aspects of data representation that have hitherto been either ill-defined or underexplored. We conclude by discussing key research challenges, which emerged from the exploration of the design space and point out future research topics.