Recent work in computational and cognitive neuroscience depicts the brain as an ever-active prediction machine: an inner engine continuously striving to anticipate the incoming sensory barrage. I briefly introduce this class of models before contrasting two ways of understanding the implied vision of mind. One way (Conservative Predictive Processing) depicts the predictive mind as an insulated inner arena populated by representations so rich and reconstructive as to enable the organism to 'throw away the world'. The other (Radical Predictive Processing) stresses the use of fast and frugal, action-involving solutions of the kind highlighted by much work in robotics and embodied cognition. But it goes further, by showing how predictive schemes can combine frugal and more knowledge-intensive strategies, switching between them fluently and continuously as task and context dictate. I end by exploring some parallels with work in enactivism, and by noting a certain ambivalence concerning internal representations and their role in the predictive mind.