This paper deals with the question: What are the criteria that an adequate theory of computation has to meet? (1) Smith’s answer: it has to meet the empirical criterion (i.e. doing justice to computational practice), the conceptual criterion (i.e. explaining all the underlying concepts) and the cognitive criterion (i.e. providing solid grounds for computationalism). (2) Piccinini’s answer: it has to meet the objectivity criterion (i.e. identifying computation as a matter of fact), the explanation criterion (i.e. explaining the computer’s behaviour), the right things compute criterion, the miscomputation criterion (i.e. accounting for malfunctions), the taxonomy criterion (i.e. distinguishing between different classes of computers) and the empirical criterion. (3) Von Neumann’s answer: it has to meet the precision and reliability of computers criterion, the single error criterion (i.e. addressing the impacts of errors) and the distinction between analogue and digital computers criterion. (4) “Everything” computes answer: it has to meet the implementation theory criterion by properly explaining the notion of implementation.