The successful implementation of Human–Robot Collaboration (HRC) has become a prominent feature of smart manufacturing environments. Key industrial requirements, such as flexibility, efficiency, collaboration, consistency, and sustainability, present pressing HRC needs in the manufacturing sector. This paper provides a systemic review and an in-depth discussion of the key technologies currently being employed in smart manufacturing with HRC systems. The work presented here focuses on the design of HRC systems, with particular attention given to the various levels of Human–Robot Interaction (HRI) observed in the industry. The paper also examines the key technologies being implemented in smart manufacturing, including Artificial Intelligence (AI), Collaborative Robots (Cobots), Augmented Reality (AR), and Digital Twin (DT), and discusses their applications in HRC systems. The benefits and practical instances of deploying these technologies are showcased, emphasizing the substantial prospects for growth and improvement in sectors such as automotive and food. However, the paper also addresses the limitations of HRC utilization and implementation and provides some insights into how the design of these systems should be approached in future work and research. Overall, this paper provides new insights into the current state of HRC in smart manufacturing and serves as a useful resource for those interested in the ongoing development of HRC systems in the industry.