In the 11th and 12th centuries the Normans had a formative influence on the development of states and societies in the British Isles, southern Italy and the Levant. Their achievements still resonate powerfully today, and represent a vital field of historical study. But how far did colonial elites define themselves as Norman, and to what extent were they categorized as such by others? What were the defining attributes of the supremacies achieved by the Normans, and by other incomers associated with them, and how decisive and diverse was the impact of their influence on local power-structures and native societies? How readily did they reach accommodations with those societies, and how might their own identities be renegotiated within the context of cross-cultural encounters?.