Communication using manual (hand) gestures is considered a defining property of social robots, and their physical embodiment and presence, therefore we see a need for a comprehensive overview of the state of the art in social robots that use gestures. This systematic literature review aims to address this need by (1) describing the gesture production process of a social robot, including the design and planning steps, and (2) providing a survey of the effects of robot-performed gestures on human-robot interactions in a multitude of domains. We identify patterns and themes from the existing body of literature, resulting in nine outstanding questions for research on robot-performed gestures regarding: developments in sensor technology and AI, structuring the gesture design and evaluation process, the relationship between physical appearance and gestures, the effects of planning on the overall interaction, standardizing measurements of gesture ‘quality’, individual differences, gesture mirroring, whether human-likeness is desirable, and universal accessibility of robots. We also reflect on current methodological practices in studies of robot-performed gestures, and suggest improvements regarding replicability, external validity, measurement instruments used, and connections with other disciplines. These outstanding questions and methodological suggestions can guide future work in this field of research.