This paper provides an overview of collaborative robotics towards manufacturing applications. Over the last decade, the market has seen the introduction of a new category of robots—collaborative robots (or “cobots”)—designed to physically interact with humans in a shared environment, without the typical barriers or protective cages used in traditional robotics systems. Their potential is undisputed, especially regarding their flexible ability to make simple, quick, and cheap layout changes; however, it is necessary to have adequate knowledge of their correct uses and characteristics to obtain the advantages of this form of robotics, which can be a barrier for industry uptake. The paper starts with an introduction of human–robot collaboration, presenting the related standards and modes of operation. An extensive literature review of works published in this area is undertaken, with particular attention to the main industrial cases of application. The paper concludes with an analysis of the future trends in human–robot collaboration as determined by the authors.