Digital Twins are conceptualized as real-time digital representations of real-life physical entities or systems. They are explored for a wide array of societal implementations, and in particular to help address fundamental societal challenges. As accurate digital equivalents of their real-life twin, Digital Twins substitute their physical twin in knowledge production and decision-making processes. They raise high expectations: they are expected to produce new knowledge, expose issues early, predict future behavior, and help to optimize the physical twin. Data play a key role here because they form the building blocks from which the Digital Twin representation is created. However, data are not neutral phenomena but products of human-technology interaction. In this article, we therefore raise the question of how a Digital Twin data collection is created, and what implications does this have for Digital Twins? To answer this question, we explore the data collection process in three cases of Digital Twin development at a university. Connecting to Jasanoff's theoretical framework of regimes of sight, we approach the creation of a data collection as acts of seeing and recording that influence how reality is represented in data, as well as give a certain legitimacy and authority to the data collection. By examining the acts of seeing and recording and their respective roles in producing the data collection, we provide insight into the struggles of representation in Digital Twins and their implications.