The increasing presence of robots in our society raises questions about how these objects are perceived by users. Individuals seem inclined to attribute human capabilities to robots, a phenomenon called anthropomorphism. Contrary to what intuition might suggest, these attributions vary according to different factors, not only robotic factors (related to the robot itself), but also situational factors (related to the interaction setting), and human factors (related to the user). The present review aims at synthesizing the results of the literature concerning the factors that influence anthropomorphism, in order to specify their impact on the perception of robots by individuals. A total of 134 experimental studies were included from 2002 to 2023. The mere appearance hypothesis and the SEEK (sociality, effectance, and elicited agent knowledge) theory are two theories attempting to explain anthropomorphism. According to the present review, which highlights the crucial role of contextual factors, the SEEK theory better explains the observations on the subject compared to the mere appearance hypothesis, although it does not explicitly explain all the factors involved (e.g., the autonomy of the robot). Moreover, the large methodological variability in the study of anthropomorphism makes the generalization of results complex. Recommendations are proposed for future studies.