The two main waves of European expansion—those of the Renaissance and of the nineteenth century—cannot simply be explained in economic terms. The high degree of risk and uncertainty associated with overseas ventures meant that they were less than fully rational. An explanation must begin by considering how the Europeans defined the extra-European world, how they defined the exotic. This article analyzes European reactions to two giraffes—one given to Lorenzo de' Medici of Florence in 1486 and the other to King Charles X of France in 1827. A comparison is made with the Chinese reactions to two giraffes that appeared in Beijing in the early fifteenth century.