Collaborative robots (cobots) have emerged as a pivotal paradigm for the upcoming leap to Industry 5.0. In recent years, the range of applications has expanded significantly, particularly in assembly tasks within the manufacturing industry. The primary goal of this paper is to review the application of cobots in industrial assembly tasks, highlighting possibilities for innovative research in smart robotics, including prospects for challenging applications in aircraft final assembly processes. The paper systematically reviews recent literature to analyse the use of collaborative robotics in industrial assembly tasks, encompassing characterisation of application environments, motivations, characteristics and outcomes of relevant use cases across various industrial segments. Additionally, it reviews a set of innovative technological patents issued by the aeronautical industry over the past 14 years, highlighting trending projects in industry. The investigation reveals that the automotive and electronics industries remain at the forefront of cobot applications, mainly for tasks like pick-and-place operations and component manipulation. Applications in open work cells, where humans and robots operate at supportive or sequential interaction levels, using conventional communication interfaces and camera-assisted technologies, have been the most prevalent. The review identifies potential opportunities and key aspects from future application scenarios for cobots. The findings are relevant to the industrial robotics community, emphasising the need for novel applied research on human–robot colla boration in aeronautical industry.