In common with much contemporary discourse around big data, recent discussion of datafication in the Journal of Strategic Information Systems has focused on its effects on individuals, organisations and society. Generally missing from such analysis, however, is any consideration of data themselves. What is it that is having these effects? In this Viewpoint article I therefore present a critical analysis of a number of widely-held assumptions about data in general and big data in particular. Rather than being a referential, natural, foundational, objective and equal representation of the world, it will be argued, data are partial and contingent and are brought into being through situated practices of conceptualization, recording and use. Big data are also not as revolutionary voluminous, universal or exhaustive as they are often presented. Some initial implications of this reconceptualization of data are explored. A distinction is made between “data in principle” as they are recorded, and the “data in practice” as they are used. It is only the latter, typically a small and not necessarily representative subset of the former, that will contribute directly to the effects of datafication.