This review is dedicated to the advanced applications of robotic technologies in the industrial field. Robotic solutions in areas with non-intensive applications are presented, and their implementations are analysed. We also provide an overview of survey publications and technical reports, classified by application criteria, and the development of the structure of existing solutions, and identify recent research gaps. The analysis results reveal the background to the existing obstacles and problems. These issues relate to the areas of psychology, human nature, special artificial intelligence (AI) implementation, and the robot-oriented object design paradigm. Analysis of robot applications shows that the existing emerging applications in robotics face technical and psychological obstacles. The results of this review revealed four directions of required advancement in robotics: development of intelligent companions; improved implementation of AI-based solutions; robot-oriented design of objects; and psychological solutions for robot–human collaboration.