In Chapter 1, I argued that the world in which we live is both complex and full of inequalities. Trends towards such complexity (which subsume inequalities of wealth, gender, etc.) have been the focus of interest among scholars since the eighteenth century, before the social sciences came into existence. Evolutionary sequences of society and culture have been proposed since then, whether based on living or past societies. Since the 1960s archaeologists have wrestled with concepts of society and social evolution (although some prefer the, to them, less loaded word ‘change’), as we have seen in Chapter 3. Disagreements in Anglo-American archaeology are clearly visible in deﬁnitions of society, in the motors of social change, in the form such change takes and in the scales of analysis which are required to study that change. At the same time, there are various terms that are used widely in the literature, and which have been mentioned in Chapter 3, but which have yet to be deﬁned. In this chapter I will focus on the deﬁnition of such terms, and on their use in the study of both contemporary and past societies. I hope this will enable the reader to negotiate his/her way through a potential terminological mineﬁeld and to understand the obsession with the dichotomous thinking that pervades social thought. According to this, societies are either egalitarian or not, hierarchical or not, and simple or complex. I will begin with concepts of equality and inequality, egalitarian and stratiﬁed, hierarchical and heterarchical, before considering the concept of complexity.