In this chapter, I will investigate the arguments for the supervenience of the mental on the physical. Before entering into the arguments themselves, I will clarify the assumption which lies at the foundation of the entire discussion. As in the field of ethics, the distinction between mental and physical predicates in philosophy of mind is not well defined. For the purpose of this discussion, the existing consensus on the status of specific predicates—their being either physical or mental—is sufficient. As long as there are two domains of predicates, the question of their relation to each other is significant, and the supervenience thesis is a possible answer to this question. If, for example, the physics of the future or the ideal physics will include mental predicates in a way that will not allow for any distinction between these and physical predicates, the question of their relation to one another is likely to disappear, since we will be left with only one domain. As long as this is not the case (and to my mind, there is no reason to believe that it will be), supervenience is a significant and reasonable thesis, and this chapter will focus on attempts to explain its source.