The use of innovative technology in the field of Speech and Language Therapy (SLT) has gained significant attention nowadays. Despite being a promising research area, Socially Assistive Robots (SARs) have not been thoroughly studied and used in SLT. This paper makes two main contributions: firstly, providing a comprehensive review of existing research on the use of SARs to enhance communication skills in children and adolescents. Secondly, organizing the information into tables that categorize the interactive play scenarios described in the surveyed papers. The inclusion criteria for play scenarios in the tables are based only on their effectiveness for SLT proven by experimental findings. The data, systematically presented in a table format, allow readers to easily find relevant information based on various factors, such as disorder type, age, treatment technique, robot type, etc. The study concludes that the despite limited research on the use of social robots for children and adolescents with communication disorders (CD), promising outcomes have been reported. The authors discuss the methodological, technical, and ethical limitations related to the use of SARs for SLT in clinical or home environments, as well as the huge potential of conversational Artificial Intelligence (AI) as a secondary assistive technology to facilitate speech and language interventions.