The wire harness assembly process is a complicated manufacturing activity, which is becoming more complex because of the evolving nature of mechatronic and electronic products that require more connectors, sensors, controllers, communication networking, etc. Furthermore, the demand for wire harnesses continues to grow in all industries worldwide as the majority of equipment, appliances, machinery, vehicles, etc., are becoming “smart” (i.e., more mechatronic or electronic). Moreover, most of the wire harness assembly process tasks are done manually, and most of these are considered non-ergonomic for human assembly workers. Hence, the wire harness manufacturing industry is faced with the challenge of increasing productivity while improving the occupational health of its human assembly workers. The purpose of this paper is to conduct a literature review exploring the state of the use of collaborative robots in the wire harness assembly process due to their potential to reduce current occupational health problems for human assembly workers and increase the throughput of wire harness assembly lines, and to provide main findings, discussion, and further research directions for collaborative robotics in this application domain. Eleven papers were found in the scientific literature. All papers demonstrated the potential of collaborative robots to improve the productivity of wire harness assembly lines, and two of these in particular on the ergonomics of the wire harness assembly process. None of the papers reviewed presented a cost–benefit or a cycle time analysis to qualitatively and/or quantitatively measure the impact of the incorporation of collaborative robots in the wire harness assembly process. This represents an important area of opportunity for research with relevance to industry. Three papers remark on the importance of the integration of computer vision systems into a collaborative wire harness assembly process to make this more versatile as many types of wire harnesses exist. The literature review findings call for further research and technological developments in support of the wire harness manufacturing industry and its workers in four main categories: (i) Collaborative Robotics and Grippers, (ii) Ergonomics, (iii) Computer Vision Systems, and (iv) Implementation Methodologies.