In the future, autonomous social robots are expected to seamlessly integrate into our society. To be perceived as interactive partners rather than mere tools, these robots must be embodied and capable of navigating complex, dynamic environments. This study explores the critical role of embodiment and examines the application of human-inspired socio-cognitive mechanisms in embodied agents. We conducted a systematic scoping review of 36 publications sourced from Scopus, IEEE Xplore, Web of Science, and PubMed. Our findings reveal a diverse array of human-inspired implementations in embodied agents, including curiosity-driven learning, categorical thinking, and predictive learning. Notably, human-like eye-gaze plays a crucial role in enhancing the anthropomorphism of these agents. By drawing inspiration from human interactions, we can transition from pre-programmed robots to fully autonomous agents that exhibit emergent behaviours and adapt to ever-changing conditions. Embodiment allows agents to communicate their intentions and desires through various modes, facilitating richer interactions. Additionally, multiple studies underscore the importance of using embodied agents to study human behaviours. Furthermore, the choice of embodiment type must depend on the task at hand; for some tasks, virtual embodiment is more effective, while for others, physical embodiment is preferable. This review provides a comprehensive starting point for future researchers interested in developing human-inspired embodied agents.