Graphs and graphing are constitutive of the sciences. Although there are an increasing number of studies in graphing, few of these focus on graphs and graphing in the discovery sciences; and even fewer take a look at graphs and graphing in the face of the uncertainty with which scientists are confronted on a daily basis. The discovery sciences allows us to revisit existing psychological theories, which tent to theorise graphing as a mental skills and graphs as external representation that is imaged in the retina and subsequently interpreted by the brain. Anthropological studies that follow scientists, said to be experts in such "skills" as graphs and graphing, suggest that such a model for understanding graphs and graphing in inappropriate. Most recently, graphs and graphing have been analysed from cultural-historical activity theoretic (e.g. Roth 2003), perspectives (Roth and Bowen 1999, Roth et al. 2002), and social practice perspectives (Roth and McGinn 1998). In Chap. 1, I review existing study graphs and graphing in a discovery sciences presented in Part II. I end the review with the proposal to take a dynamic perspective on graphs and graphing, which radically changes the ways in which we think about the topic because the categories of thought no longer are taken to be self-identical but are of a kind that theorises graphs and graphing as continuously changing phenomena.