World Models (WM) are increasingly seen as a foundation for intelligent agents that can predict, plan, and act beyond their training distribution. In this paper, we study WMs from a causal perspective across multiple levels of abstraction, ranging from perceptual observations to building a conceptual representation of the structure governing the environment dynamics. We argue that useful WMs must go beyond generative capabilities alone: they should also capture entity properties, entity-to-entity interactions, and entity-to-environment interactions that determine and explain the dynamics of a system. We provide a formal definition of Causal WMs (CWMs) grounded in the tasks they are intended to support, connecting world modelling with existing work in causal representation learning, object-centric learning, causal discovery, structural causal models, and model-based decision-making. Finally, we relate CWMs to the literature on identifiability, clarifying when the components of a WM can be recovered from data and up to which equivalence. With this, we ground WMs in representations and structures that support causal reasoning and informed decision-making.

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