This chapter examines three aspects of science in the context of the Iberian Atlantic of the sixteenth century. First, it investigates the exploration of the New World via its relation with the traditional idea of modern science. Next the chapter looks at the encounter of cultures and the European appropriation of fields of American knowledge. Finally, it argues that the notion of comprehension , understood both as a process of appropriation and as a form of self-construction, can help improve our understanding of the history of the encounter between Europe and the New World. All these elements are interconnected and are directly related to the construction of a Eurocentric world order. Sixteenth century Iberian science in the New World, natural history, cartography and studies on population, was a major attempt at inclusion and translation of the unknown into a familiar world picture. Keywords: Eurocentric world order; European appropriation; Iberian Atlantic; New World; notion of comprehension ; sixteenth century; traditional idea of modern science