Predictive processing (PP) approaches to the mind are increasingly popular in the cognitive sciences. This surge of interest is accompanied by a proliferation of philosophical arguments, which seek to either extend or oppose various aspects of the emerging framework. In particular, the question of how to position predictive processing with respect to enactive and embodied cognition has become a topic of intense debate. While these arguments are certainly of valuable scientific and philosophical merit, they risk underestimating the variety of approaches gathered under the predictive label. Here, we first present a basic review of neuroscientific, cognitive, and philosophical approaches to PP, to illustrate how these range from solidly cognitivist applications – with a firm commitment to modular, internalistic mental representation – to more moderate views emphasizing the importance of ‘body-representations’, and finally to those which fit comfortably with radically enactive, embodied, and dynamic theories of mind. Any nascent predictive processing theory (e.g., of attention or consciousness) must take into account this continuum of views, and associated theoretical commitments. As a final point, we illustrate how the Free Energy Principle (FEP) attempts to dissolve tension between internalist and externalist accounts of cognition, by providing a formal synthetic account of how internal ‘representations’ arise from autopoietic self-organization. The FEP thus furnishes empirically productive process theories (e.g., predictive processing) by which to guide discovery through the formal modelling of the embodied mind.