Recognizing the distributed nature of agency in human–AI interactions, this article proposes a framework for examining the power dynamics that undergird the use of generative AI (GenAI) for language learning. Drawing on Darvin and Norton’s model of investment, it adopts a critical sociomaterial lens to cast a light on the entanglement of bodies, objects and discourse in these interactions, while highlighting how issues of positioning, access to resources, and ideological reproduction emerge from this perspective. Human agency both interacts with and is constrained or amplified by the functionalities of GenAI. To invest in agentive GenAI practices that enable meaningful learning and the achievement of their own intentions, learners must not only recognize the power of GenAI to steer interactions and promote specific ways of thinking, but also resist fully delegating the production of meaning and texts to technology. Cultivating critical digital literacies that recognize how power operates in human-AI interactions is integral to fostering reflexive, inclusive and equitable language learning and teaching in the age of GenAI.