To achieve recycling of mixed industrial waste toward an advanced sustainable society, waste sorting automation through robots is crucial and urgent. For this purpose, a robot is required to recognize the category, shape, pose, and condition of different waste items and manipulate them according to the category to be sorted. This survey considers three potential difficulties in the sorting automation: 1) End-effector: to robustly grasp and manipulate different waste items with dirt and deformations; 2) Sensor: to recognize the category, shape, and pose of existing objects to be manipulated and the wet and dirty conditions of their surfaces; and 3) Planner: to generate feasible and efficient sequences and trajectories. This survey includes 76 references to studies related to automatic waste sorting and 159 references to worldwide waste recycling attempts. This pioneering investigation reveals the possibility and limitations of conventional systems; thus, providing insights on open issues and potential technologies to achieve a robot-incorporated sorter for the chaotic mixed waste is one of its contributions. This paper further presents a system design policy for readers and discusses future advanced sorters, thereby contributing to the field of robotics and automation. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Most automated sorting systems operate for limited target waste items. This study is motivated by the automation of mixed industrial waste treatment facilities using advanced robotic sorters. Emerging advances and increasing functionalities of robot system components will widen system applicability and increase use cases in the chaotic mixed industrial waste domain. This paper surveys the research conducted to date, discusses open issues and potential approaches, and presents user guides that provide practitioners with a system design policy. The user guides created according to the strengths and weaknesses of each system configuration provide future researchers and developers with a useful a priori design policy that has been thus far validated on efficiency, quality, productivity, and reliability. A question-and-answer style guide and a sorting-target-aware previous study reference list allows users to find the desired system configuration, including the investigated components according to their purpose.