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Establishing and leveraging equivalence is a central practice in mathematics. Though there have been many studies of students’ uses of equivalence, much of the research thus far has been domain-specific, and the literature generally lacks coherence within and across mathematical domains. In this theoretical paper, we propose an initial unifying framework for capturing the different ways that students might establish equivalence. Using constructs born out of the K-12 literature, we discuss how this framework can be applied to student reasoning in undergraduate settings. We do so by presenting the results of conceptual analyses of students’ possible uses of equivalence when thinking about vectors, isomorphisms and homeomorphisms, and single- variable limits. We then conclude with a detailed analysis of student data from combinatorics that identifies productive aspects of their uses of equivalence when constructing permutations.