Given recent technological developments in robotics, artificial intelligence and virtual reality, it is perhaps unsurprising that the arrival of emotionally expressive and reactive artificial agents is imminent. However, if such agents are to become integrated into our social milieu, it is imperative to establish an understanding of whether and how humans perceive emotion in artificial agents. In this review, we incorporate recent findings from social robotics, virtual reality, psychology, and neuroscience to examine how people recognize and respond to emotions displayed by artificial agents. First, we review how people perceive emotions expressed by an artificial agent, such as facial and bodily expressions and vocal tone. Second, we evaluate the similarities and differences in the consequences of perceived emotions in artificial compared to human agents. Besides accurately recognizing the emotional state of an artificial agent, it is critical to understand how humans respond to those emotions. Does interacting with an angry robot induce the same responses in people as interacting with an angry person? Similarly, does watching a robot rejoice when it wins a game elicit similar feelings of elation in the human observer? Here we provide an overview of the current state of emotion expression and perception in social robotics, as well as a clear articulation of the challenges and guiding principles to be addressed as we move ever closer to truly emotional artificial agents.