This dissertation examines the relationship between theory and practice in the exercise of imperial sovereignty, including during the height of Iberian global hegemony in the late sixteenth and early seventeenth centuries. It focuses in particular on remote regions of the Spanish and Portuguese empires. The manuscript opens with an analysis of a range of influential treatises, chronicles, epic poetry, cartography, and iconography, which glorified, amplified, and aimed to legitimize the claims and aspirations of the Iberian rulers to imperium beyond Europe. These texts coalesced to form a common, uniquely Iberian discourse of empire, which crystallized around the turn of the seventeenth century, during the union of the Spanish and Portuguese crowns. Then, through case studies on Southeast Africa, the Philippines, and the Rio de la Plata, the study explores how complex jurisdictional layering, physical distance, and the power of indigenous and local settler groups created situations in which, beyond official centers of colonial power, the crown's effective sovereignty was diffuse, highly circumscribed, and constantly fluid in its geography. Beyond highlighting this dissonant tension between ambition and effective rule, the dissertation demonstrates how, in different moments, local actors on the peripheries of empire rearticulated concepts of Iberian and broader European law and political theory, either to affirm their obedience and belonging within the larger imperial body, or to claim authority as sources of law in their own right and defend their autonomy against the extension of crown power.