Robot manipulation of multiple objects is an important topic for applications including warehouse automation, service robots performing cleaning, and large-scale object sorting. Although problems can range in complexity from a few objects to large disordered piles, autonomy remains a significant technical challenge due to the high-dimensional joint configuration space of the robot and all objects, the complex dynamics of object interaction, and the ambiguity and occlusion caused by clutter. This article surveys a broad range of classical and state-of-the-art research in multiobject manipulation and categorizes them along the dimensions of tasks, perception, predictive models, and decision-making algorithms. It also covers emerging trends and open problems faced in the ongoing effort to realize robust multiobject manipulation systems in practice.