What role do affective feelings (feelings/emotions/moods) play in adaptive behaviour? What are the implications of this for understanding and developing artificial general intelligence? Leading theoretical models of brain function are beginning to shed light on these questions. While artificial agents have excelled within narrowly circumscribed and specialised domains, domain-general intelligence has remained an elusive goal in artificial intelligence research. By contrast, humans and nonhuman animals are characterised by a capacity for flexible behaviour and general intelligence. In this article I argue that computational models of mental phenomena in predictive processing theories of the brain are starting to reveal the mechanisms underpinning domain-general intelligence in biological agents, and can inform the understanding and development of artificial general intelligence. I focus particularly on approaches to computational phenomenology in the active inference framework. Specifically, I argue that computational mechanisms of affective feelings in active inference—affective self-modelling—are revealing of how biological agents are able to achieve flexible behavioural repertoires and general intelligence. I argue that (i) affective self-modelling functions to “tune” organisms to the most tractable goals in the environmental context; and (ii) affective and agentic self-modelling is central to the capacity to perform mental actions in goal-directed imagination and creative cognition. I use this account as a basis to argue that general intelligence of the level and kind found in biological agents will likely require machines to be implemented with analogues of affective self-modelling.