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This chapter considers action-oriented processing from a model-oriented standpoint. Possible relationships between action and cognition are reviewed in abstract or conceptual terms. We then turn to models of their interrelationships and role in mediating cognitively enriched behaviors. Examples of theories or models inspired by the actionoriented paradigm are briefly surveyed, with a particular focus on ideomotor theory and how it has developed over the past century. Formal versions of these theories are introduced, drawing on formulations in systems biology, information theory, and dynamical systems theory. An attempt is made to integrate these perspectives under the enactivist version of the Bayesian brain; namely, active inference. Implications of this formalism and, more generally, of action-oriented views of cognition are discussed, and open issues that may be usefully pursued from a formal perspective are highlighted.