The topic of mental state attribution to robots has been approached by researchers from a variety of disciplines, including psychology, neuroscience, computer science, and philosophy. As a consequence, the empirical studies that have been conducted so far exhibit considerable diversity in terms of how the phenomenon is described and how it is approached from a theoretical and methodological standpoint. This literature review addresses the need for a shared scientific understanding of mental state attribution to robots by systematically and comprehensively collating conceptions, methods, and findings from 155 empirical studies across multiple disciplines. The findings of the review include that: (1) the terminology used to describe mental state attribution to robots is diverse but largely homogenous in usage; (2) the tendency to attribute mental states to robots is determined by factors such as the age and motivation of the human as well as the behavior, appearance, and identity of the robot; (3) there is a computer < robot < human pattern in the tendency to attribute mental states that appears to be moderated by the presence of socially interactive behavior; (4) there are conflicting findings in the empirical literature that stem from different sources of evidence, including self-report and non-verbal behavioral or neurological data. The review contributes toward more cumulative research on the topic and opens up for a transdisciplinary discussion about the nature of the phenomenon and what types of research methods are appropriate for investigation.