Our understanding of the neural basis of consciousness has substantially improved in the last few decades. New imaging and statistical techniques have been introduced, experiments have become more sophisticated, and several unsuccessful hypotheses have been quite conclusively ruled out. However, neuroscientists still do not entirely agree on the critical neural features required for sustaining perceptual conscious experiences in humans and other primates. This chapter discusses a selection of influential views of the neural correlates of consciousness and the predictions they make. By highlighting some neurobiological and computational modelling results, it will be argued that the currently available evidence favors a hierarchical processing architecture that confers a crucial, if subtle and specific, role to prefrontal cortex.