Assessment of student learning is commonly understood as a seemingly objective measurement of learning outcomes. It is seen as fair that assessment targets students' abilities -- not their identities or personalities. This idea fails to acknowledge how assessment transforms its object, the students, often in unintended ways. While higher education research has largely emphasised the impact of assessment on student learning, the ontological question of how assessment shapes students has remained marginal. This is despite assessment being a part of the fabric of life in higher education: examinations, assignments, grades, rubrics, rankings, and metrics characterise the student experience. The present study addresses this knowledge gap by reviewing empirical studies on how assessment shapes student identities through a theory-driven integrative review of 32 articles (2007-2023). First, these studies are summarised to understand how they conceptualise 'identities', what kinds of assessment practices they depict, and what the reported influences on student identities are. Second, a conceptual synthesis provides a metatheory on how assessment transforms student identities in higher education. This theorisation suggests that assessment shapes students through the ontological mechanisms of (1) gatekeeping, (2) legitimisation, (3) concretisation, (4) socialisation and (5) individualisation. Moreover, the theorisation considers students' own agency over their identity development. Overall, this study emphasises the crucial, hitherto overlooked role of assessment in shaping students' professional and personal identities in higher education. This study proposes a research agenda to better understand student identity formation in and through assessment.