Recently, the mechanistic framework of active inference has been put forward as a principled foundation to develop an overarching theory of consciousness which would help address conceptual disparities in the field (Wiese 2018; Hohwy and Seth 2020). For that promise to bear out, we argue that current proposals resting on the active inference scheme need refinement to become a process theory of consciousness. One way of improving a theory in mechanistic terms is to use formalisms such as computational models that implement, attune and validate the conceptual notions put forward. Here, we examine how computational modelling approaches have been used to refine the theoretical proposals linking active inference and consciousness, with a focus on the extent and success to which they have been developed to accommodate different facets of consciousness and experimental paradigms, as well as how simulations and empirical data have been used to test and improve these computational models. While current attempts using this approach have shown promising results, we argue they remain preliminary in nature. To refine their predictive and structural validity, testing those models against empirical data is needed i.e., new and unobserved neural data. A remaining challenge for active inference to become a theory of consciousness is to generalize the model to accommodate the broad range of consciousness explananda; and in particular to account for the phenomenological aspects of experience. Notwithstanding these gaps, this approach has proven to be a valuable avenue for theory advancement and holds great potential for future research. <<<