As robots are increasingly important in human’s life, people begin to pay attention to their other potentials besides intelligence, such as empathy, which plays an important role in human sociality. The prerequisite for robots to become our partner is to share and understand the human’s emotions and to react properly. In fact, current research on empathy mostly focuses on traditional interpersonal interaction, and little attention has been given to human-robot interaction. This paper aims to review related research on psychology and human-robot interaction under the background of developing artificial intelligence. Russian Doll Model and Dual-Process Model have been two most influential theoretical models of empathy. Russian Doll Model considers empathy as a construct comprising of three layers: (1) motor mimicry and emotional contagion; (2) empathetic concern and consolation; (3) perspective-taking and targeted helping. Dual-Process Model stems from relevant findings in cognitive neuroscience, and proposes that empathy work via two routes: bottom-up processing and top-down processing. Both models as well as empirical studies drawing from them suggest a possibility to program artificial empathy analogous to human empathy. Focusing on the topic of artificial empathy and based on classic models, the current study reviewed the latest research in artificial intelligence and systematically discussed existing theoretical models and empirical studies about artificial empathy. First, we did a bibliometric analysis to draw an overall picture of artificial empathy studies. By analyzing 175 articles, we found that studies in the field of artificial empathy were expanding concentrated on three topics: (1) interface and form of human-robot interaction; (2) computerized simulation of empathy; (3) artificial intelligence. Second, we introduced two computerized models of artificial empathy. As mentioned above, these two models were derived from the traditional empathy models and assumed that robots needed a main system of empathy and another system for learning. Recently, preliminary application of research in artificial empathy has been successful in board game industry and medical treatment. In order to promote further research, we argue that it is important to draw on progress in four areas below: (1) Due to the importance of self-learning, insights from developmental studies would contribute to building theoretical models and developing scales with satisfactory psychometric properties in the field of artificial empathy; (2) According to the results of bibliometric analysis, interdisciplinary cooperation would help to delve deep into this field; (3) ethical issues should not be neglected as studies on artificial empathy proceed, since there is still so much work to do on these issues and government participation is indispensible; (4) Last but not least, consciousness is a hot topic in the field of artificial intelligence. It is possible that authentic empathy cooccurs with consciousness, and if which is exactly the case we would have to consider the role of consciousness in developing artificial empathy. In sum, based on the present research achievement and theory models, we propose that the actualization of artificial empathy will be the key for robots to open the door towards the real human-like and to better serve humans in the future.