Anthropomorphism is a way of making sense of complex behavior in the world around us. It is not one process, but involves several -- quite independent -- levels, e.g., primitive psychology, folk-psychology, social stereotypes and emotional anthropomorphism. This paper explores psychological and anthropological research into the different layers in order to better understand anthropomorphic processes triggered by computer interfaces and systems. Each level is exemplified by existing systems. In conclusion, when referring to anthropomorphism -- for instance in relation to an interface or system -- we must be clear about which level we indicate, since each has its own characteristics and involves specific types of user expectations.