Children with autism spectrum disorder (ASD) have deficits in the socio-communicative domain and frequently face severe difficulties in the recognition and expression of emotions. Existing literature suggested that children with ASD benefit from robot-based interventions. However, studies varied considerably in participant characteristics, applied robots, and trained skills. Here, we reviewed robot-based interventions targeting emotion-related skills for children with ASD following the guidelines of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. We systematically searched for all relevant articles published in English language until April 2021, using the databases Scopus, Web of Science, and PubMed. From a total of 609 identified papers, 60 publications including 50 original articles and 10 non-empirical articles including review articles and theoretical articles were eligible for the synthesis. A total of 892 participants were included in the robot-based intervention studies; 570 of them were children with ASD. Nao and Zeca were the most frequently used robots; Recognition of basic emotions and getting into interaction were the most frequently trained skills; while happiness, sadness, fear, and anger were the most frequently trained emotions. The studies reported a wide range of challenges with respect to robot-based intervention, ranging from limitations for certain ASD subgroups and security aspects of the robots to efforts regarding the automatic recognition of the children's emotional state by the robotic systems. Finally, we summarised and discussed recommendations regarding the application of robot-based interventions for children with ASD.