The evolution of Human-Robot Collaboration (HRC) has moved beyond simple task-sharing, progressing toward advanced systems that integrate cognitive and physical dimensions in a proactive approach. The prevailing research is increasingly emphasizing adaptive interaction, predictive intelligence, multimodal perception and mutual synchronization between humans and robots. In this study, a literature mapping review was conducted to capture the latest trends and practices in HRC design and control, also distinguishing human-centric from robot-centric approaches. The analysis identified five thematic clusters capturing the current trends, i.e.: (i) AI-driven cognitive augmentation; (ii) seamless safety; (iii) enhanced digital twins, augmented reality, and virtualization; (iv) multimodal perception and mutual awareness; and (v) robot humanization. A literature key gap emerged, i.e., the lack of a holistic, system-centric framework that comprehensively integrates both human and robotic perspectives, in system design and control principles as per the identified dimensions. To address the gap, the Human-Robot Embodiment paradigm is introduced and proposed as the evolution of proactive HRC, structured around three integrated dimensions: (a) Situational Awareness and Continual Learning, (b) Enactment and Entrainment and (c) Bidirectional Control. The paper concludes by outlining challenges, opportunities and future directions for implementing the unified HRE paradigm.