What can a small group of extraordinary, heart shaped world maps tell us about the exploration of the New World in the 16th century? Long fascinating to those who study cartography, the cordiform maps (from the Latin for heart, cor) are known to few outside that small group. Their heart shape has been considered something of an anomaly, sitting uncomfortably with the discoveries and discourses of the New World or the genesis of modern cartography. There are very few convincing accounts of the maps’ purpose in their own time. Why world maps were made shaped after the human heart is a story that needs to be told, as the concepts and ideals of those engaged with the project of European exploration and expansion still demands greater understanding today. This new research has two interpretative aims. The first is to ask why the shape of a heart was chosen for imaging the world. To do this requires exploring shifting meanings for the heart image at each moment of its cartographic iteration. This approach sees the map not as a fixed sign, judged by its geographic content alone, but a complex image under pressure from wider expectations upon the mapmakers and their audiences. J. B. Harley once called for more understanding for the role of decoration within cartography; these maps may shift analysis towards a greater emphasis on the wider functions of imaging practices. The second aim is to establish that the maps’ shape is intimately entangled with aspirations about the New World. A 1531 double cordiform map was the first to use the term Terra Australis Incognita, depicting an astonishingly shaped southern continent long before Europeans had visited those regions. In the sixteenth century, meanings were attributed to the heart that we no longer subscribe to today, including learning and memory, leadership and wisdom. The most celebrated cordiform map is scripted in Ottoman Arabic, probably commissioned for Suleiman the Magnificent, invigorating connections between European and Ottoman worldviews. Ultimately, these unusual maps can illuminate the mindset of those in Europe aspiring to a new vision of human affairs, suggesting that the early modern cartographic enterprise was not as homogenous as is often considered. Imaging the world, like the heart, was not then as we know it today; with two mapmakers imprisoned on life-threatening charges, a heart shaped world carried potentially unorthdox propositions. This paper introduces audiences to the maps and the key issues in interpretation. It will show that they, perhaps more than any other maps of their time, are critical for revealing potentially conflicting and controversial aspirations for the New World.