This paper analyses the changing conceptualisation of cellular differentiation during the twentieth century. This involved a move away from a view of this process as irreversible to an understanding of it as contingent. We examine the import of this shift for the transformation of stem cell biology, including the therapeutic promise attributed to this field, and how it came to challenge historical conceptions of both the cell and stem cell. We take as our starting point the 2012 Nobel Prize for Physiology and Medicine awarded jointly to John Gurdon and Shinya Yamanaka. In the view of the Nobel Committee, their work delineates a paradigm shift in the understanding of cellular differentiation, one that incorporates the concept of 'plasticity'. We explore the emergence, uses and meanings of this concept within this specific biological context, examining and emphasising its role as an epistemological tool. In this setting, 'plasticity' was introduced by cell biologist Helen Blau in the course of research undertaken in the 1980s into the genetics of cell differentiation. We argue that Blau's experimental and theoretical contributions were seminal to a reconceptualisation of this process and provide a crucial link between the work of Gurdon and Yamanaka. Overall, the paper highlights the contested process of conceptual change within the biomedical sciences. It also draws attention to the dynamic and reciprocal relationship between conceptual and technical change, exemplified here in the changing conceptions of cell differentiation following from the analysis of gene expression using new cell fusion and cloning techniques. More broadly, the paper also affords a window onto the shifting priorities, goals and values within late twentieth-century biomedical research.