Collaborative robotics is an umbrella term that conveys the general idea of proximity between machines and humans for some useful tasks in a shared space, with a range of options for timing (continuously, synchronously, alternately, etc.). While this type of human robot interaction is fairly common in many fields of robotics, this survey is dedicated to the technology and situations that are typical of industrial applications. The current state-of-the-art in collaborative robotics for industrial applications is the result of a long legacy of research and development in actuation principles and mechanisms from 2000s onward, together with an abundant literature about improving control performances, intuitive interaction modes, and perception with sensors. Safety technology and standardization is discussed according to the principles of risk estimation and the typical strategies for risk reduction that are suitable for different classes of robot systems are used in collaborative applications. The organization of applications (planning, role assignment, optimization of resources) has a major impact on both the quality and the safety of collaborative robotics solutions, with most of the literature focused on investigating those performance metrics that combine human factors and production figures. The survey is intended to delineate an interpretation key for the design of collaborative robotics solution that explains the relationship among all relevant factors: actuation, control, safety, physical interaction, usability, and productivity.