The notion of emergence has several meanings. In the vernacular language, emergence denotes both a gradual beginning or coming forth, or a sudden uprising or appearance; to emerge also means to become visible; for example, emergence may denote the act of rising out of a fluid. This latter sense is close to its Latin roots, where emergere is the opposite of mergere: to be submerged. In what follows, we relate the “act of rising out” to the arising of some phenomenon from a process, and note the fact that to become visible presupposes some observer. So, the common sense of emergence is linked with the meaning of a process that produces some phenomenon that might be detected by an observer. The concept of Emergence first discussed in philosophy, is also widely used in complex adaptive systems literature, especially in computer sciences (Holland, 1998) and related fields (multi-agent systems, artificial intelligence, artificial life...) as well as in physics, biology, and cognitive sciences. In a pioneering book on artificial society and multi-agent simulations in social sciences, Nigel Gilbert put the emphasis on “emergence” as a key concept of this approach: “Emergence is one of the most interesting issues to have been addressed by computer scientists over the past few years and has also been a matter of concern in a number of other disciplines, from biology to political science” (Gilbert (1995) p.8). Later, Gilbert 2002) discussed the varieties of emergent phenomena by developing Schelling’s Model of residential segregation as a case study. He put the emphasis on methodological problems linked with emergence in artificial society, such as social recognition, construction of categories, second order emergence and downward causation. These latter terms concern the process through which the macro-level emerging social structure “feedbacks” into the micro-level by re-shaping the “elementary” behaviour (also called “immergence” by Gilbert (1995). According to Castelfranchi (1998) such a downward social determination is linked with cognitive agents: the agents' minds: works as cognitive mediators for the social action Castelfranchi (2000). From a methodological point of view, emergence provides therefore concepts that allow us to encompass both holism and a reductionist version of methodological individualism. For instance, Sawyer, starting from a discussion of the emergentist approaches in philosophy, psychology and sociology Sawyer (2001), (2002) advocates a “non-reductive individualist” approach of emergence Sawyer (2002) (2003), that allows us to understand societies as complex systems Sawyer (2004), (2005). Unfortunately, these approaches remain mainly at the conceptual level and do not develop a formal framework both operative in multi-agent frameworks and that could be linked in some way with more traditional models. This latter requirement allows us to make comparative appraisal and to provide an account of how emergence could effectively break new ground and support new conceptual and formal advance. Such an assessment would be easier with the models of the economics side (Agent based Computational Economics - ACE) which can be more easily related with traditional formalisms. This is the case for instance of the ACE model of Axtell, Epstein & Young (2001) which is an extension of a population game by Young (1998). The first section raises critical questions about emergence from two paradigmatic examples of emergent phenomenon resulting from local social interaction (Schelling’s model of Segregation and the RY model of emergence of classes). The second section briefly reviews and discusses some conceptual or formal definitions of emergence from both Philosophy and Computer sciences, with a special attention for multi-agent systems (Müller 2004). The third section provides a complementary definition proposed by Bonabeau & Dessalles (1997) and discussed in Dessalles & Phan, (2007), Dessalles , Ferber & Phan (2007) to be operative in multi-agent frameworks and to make sense from both a cognitive and a social point of view. This definition is coherent with important related features, like cognitive hierarchy, detection, and complexity.