While philosophers have been debating for decades on whether different entities—including severely disabled human beings, embryos, animals, objects of nature, and even works of art—can legitimately be considered as having moral status, this question has gained a new dimension in the wake of artificial intelligence (AI). One of the more imminent concerns in the context of AI is that of the moral rights and status of social robots, such as robotic caregivers and artificial companions, that are built to interact with human beings. In recent years, some approaches to moral consideration have been proposed that would include social robots as proper objects of moral concern, even though it seems unlikely that these machines are conscious beings. In the present paper, I argue against these approaches by advocating the “consciousness criterion,” which proposes phenomenal consciousness as a necessary condition for accrediting moral status. First, I explain why it is generally supposed that consciousness underlies the morally relevant properties (such as sentience) and then, I respond to some of the common objections against this view. Then, I examine three inclusive alternative approaches to moral consideration that could accommodate social robots and point out why they are ultimately implausible. Finally, I conclude that social robots should not be regarded as proper objects of moral concern unless and until they become capable of having conscious experience. While that does not entail that they should be excluded from our moral reasoning and decision-making altogether, it does suggest that humans do not owe direct moral duties to them.