Research on affective communication for socially assistive robots has been conducted to enable physical robots to perceive, express, and respond emotionally. However, the use of affective computing in social robots has been limited, especially when social robots are designed for children, and especially those with autism spectrum disorder (ASD). Social robots are based on cognitive-affective models, which allow them to communicate with people following social behaviors and rules. However, interactions between a child and a robot may change or be different compared to those with an adult or when the child has an emotional deficit. In this study, we systematically reviewed studies related to computational models of emotions for children with ASD. We used the Scopus, WoS, Springer, and IEEE-Xplore databases to answer different research questions related to the definition, interaction, and design of computational models supported by theoretical psychology approaches from 1997 to 2021. Our review found 46 articles; not all the studies considered children or those with ASD.