The study of representation is a major research field in quantitative political science. Since the early 2000s, it has been accompanied by a range of important conceptual innovations by political theorists working on the topic. Yet, although many quantitative scholars are familiar with the conceptual literature, even the most complex quantitative studies eschew engaging with the “new wave” of more sophisticated concepts of representation that theorists have developed. We discuss what we take to be the main reasons for this gap between theory and empirics, and present four novel conceptions of representation that are both sensitive to theorists’ conceptual impulses and operationalizable for quantitative scholars. In doing so, we advance an alternative research agenda on representation that moves significantly beyond the status quo of the field.