This review emphasizes the fascinating convergence of Neuro-Symbolic AI (NeSy) and Compositional Generalization (CoGe), examining how these models might potentially transform AI by enabling real human-like intelligence. This research contends that NeSy's capacity to combine the advantages of neural and symbolic techniques has enormous potential for addressing the CoGe dilemma. CoGe necessitates the ability to learn and use information in unexpected settings through the flexible assembly of existing building components. NeSy architectures, with their distinct combination of symbolic reasoning and flexible learning, provide a viable option for overcoming this critical hurdle. In this paper, we highlighted some of the most important concepts of both NeSy and CoGe, showcasing the cutting-edge research trends shaping these fields, we delve into their diverse techniques and methods. Drawing upon cognitive science studies and concrete AI-based works, we illustrate the multitude of possibilities for implementing CoGe within NeSy. Finally, we discuss the results performed by these studies, their commonalities, we then present our proposition and address the open challenges that lie ahead on the path towards true CoGe with NeSy.