Purpose: Looking at the limits of artificial intelligence (AI) and controlling based on complexity and system-theoretical deliberations, the authors aimed to derive a future outlook of the possible applications and provide insights into a future complementary of human–machine information processing. Derived from these examples, the authors propose a research agenda in five areas to further the field. Design/methodology/approach: This article is conceptual in its nature, yet a theoretically informed semi-systematic literature review from various disciplines together with empirically validated future research questions provides the background of the overall narration. Findings: AI is found to be severely limited in its application to controlling and is discussed from the perspectives of complexity and cybernetics. A total of three such limits, namely the Bremermann limit, the problems with a partial detectability and controllability of complex systems and the inherent biases in the complementarity of human and machine information processing, are presented as salient and representative examples. The authors then go on and carefully illustrate how a human–machine collaboration could look like depending on the specifics of the task and the environment. With this, the authors propose different angles on future research that could revolutionise the application of AI in accounting leadership. Research limitations/implications: Future research on the value promises of AI in controlling needs to take into account physical and computational effects and may embrace a complexity lens. Practical implications: AI may have severe limits in its application for accounting and controlling because of the vast amount of information in complex systems. Originality/value: The research agenda consists of five areas that are derived from the previous discussion. These areas are as follows: organisational transformation, human–machine collaboration, regulation, technological innovation and ethical considerations. For each of these areas, the research questions, potential theoretical underpinnings as well as methodological considerations are provided.