Despite having been a pedigree stretching for several decades, computational approaches remain highly debated in archaeology, hailed by some as the future of the discipline, and discarded by some as a poor, arrogant and overgeneralizing attempt at mimicking the past. This introductory chapter argues that traditional criticisms made at computational models stem from several fundamental misunderstandings. In particular, several archaeologists favouring either a more "social theory" perspective or a more "fieldwork first and avoid generalizing" approach have negatively commented upon what they perceived as simple models when compared to the complex, holistic nature of social life. We argue here that modelling scientific teams, combining archaeologists and modellers, are aware of these complexity and uncertainty and rather prefer to tackle it by explicitly focusing upon a minimal set of epistemological procedures, concepts and parameters, set in an explicitly formal environment. The implications of this epistemological standpoint are evaluated in view of the various contributions to this volume, presented at the end of this contribution.