The controversial question of whether machines may ever be conscious must be based on a careful consideration of how consciousness arises in the only physical system that undoubtedly possesses it: the human brain. We suggest that the word "consciousness" conflates two different types of information-processing computations in the brain: the selection of information for global broadcasting, thus making it flexibly available for computation and report (C1, consciousness in the first sense), and the self-monitoring of those computations, leading to a subjective sense of certainty or error (C2, consciousness in the second sense). We argue that despite their recent successes, current machines are still mostly implementing computations that reflect unconscious processing (CO) in the human brain. We review the psychological and neural science of unconscious (CO) and conscious computations (C1 and C2) and outline how they may inspire novel machine architectures.