With the development of technology, robots as the main carrier of artificial intelligence will appear more and more in human life and work. However, for ordinary people, robots are still relatively new things. Under such a background, whether people accept robots, under what conditions robots are more acceptable to people, and what kind of robots are more acceptable to people are all important issues that need to be explored. Therefore, this paper focuses on the factors that affect people’s acceptance of robots. Specifically, we systematically review the influencing factors of robot acceptance from three aspects: Robot factors, human factors and human-robot interaction factors. Firstly, there is no doubt that people’s acceptance of robots is affected by the factors pertaining to robot itself. Compared with human factors, robot factors are more controllable and practical for robot designers, producers and sellers, and thus are currently the most concerned issue for the public and researchers. Secondly, characteristics of robots such as their visual features, tactile features, auditory features and behavioral features can significantly affect people’s acceptance of robots. Among these characteristics of robots, the anthropomorphism of robot appearance is a hot research issue. A series of studies indicates that the appropriate degree of anthropomorphism can increase people’s acceptance of robot, but inappropriate degree of anthropomorphism can trigger uncanny valley effect, which in turn significantly decrease robot acceptance. Capabilities of robots, such as their instrumental and social abilities have also been proved to play an important in affecting people’s acceptance of robots. The instrumental capabilities of robots are undoubtedly the basic abilities, which include not only utilitarian factors (e.g., perceived usefulness and perceived ease of use), but also hedonic factors (e.g., perceived enjoyment). The social capabilities of robots are mainly reflected on their abilities to socialize with people, which include communicating with human and expressing their social cues such as emotions and vulnerability. Secondly, human factors (e.g., demographic variables and psychological variables) influencing people’s acceptance of robots should not be neglected. Many studies demonstrate that an individual’s demographic characteristics such as age, gender, education and cultural background play an important role in robot acceptance. In general, young people, males, and those with higher education are more likely to accept robots. Individual’s psychological characteristics such as personality, personal innovativeness and self-efficacy have also been shown to have an impact on people’s acceptance of robots. Thirdly, in addition to robot factors and human factors, human-robot interaction factors affecting robot acceptance have also been paid more and more attention by researchers. Lots of studies indicate that robot-related experience can significantly influence people’s acceptance of robots. Previous experience with robots has a positive effect on users’ attitudes towards robots, trust in robots and their own self-esteem. Meanwhile, people’s perception of robots (e.g., perception of robots’ warmth, competence and social presence) is also important. Researchers have suggested that people’s perception of robots’ warmth and competence is not only relevant to their attitudes towards robots, but also can predict their specific emotional response and behavioral tendency. In sum, we systematically review possible influencing factors of robot acceptance, which include robot factors, human factors and human-robot interaction factors. Based on the theory of mind perception, we suggest that people’s acceptance of robots are both positive and negative. On the one hand, people over-trust robots because of the strong capabilities of robots. On the other hand, people also attack robots because of ignoring robots’ experience. Having considered all possible factors, we believe that anthropomorphism may be the core variable that affects people’s acceptance of robots, and the ultimate problem of robot acceptance is necessarily moral issues concerning robots.