Abstract: BACKGROUND Humans have a fantastic ability to manipulate objects of various shapes, sizes, and materials and can control the objects’ position in confined spaces with the advanced dexterity capabilities of our hands. Building machines inspired by human hands, with the functionality to autonomously pick up and manipulate objects, has always been an essential component of robotics. The first robot manipulators date back to the 1960s and are some of the first robotic devices ever constructed. In these early days, robotic manipulation consisted of carefully prescribed movement sequences that a robot would execute with no ability to adapt to a changing environment. As time passed, robots gradually gained the ability to automatically generate movement sequences, drawing on artificial intelligence and automated reasoning. Robots would stack boxes according to size, weight, and so forth, extending beyond geometric reasoning. This task also required robots to handle errors and uncertainty in sensing at run time, given that the slightest imprecision in the position and orientation of stacked boxes might cause the entire tower to topple. Methods from control theory also became instrumental for enabling robots to comply with the environment’s natural uncertainty by empowering them to adapt exerted forces upon contact. The ability to stably vary forces upon contact expanded robots’ manipulation repertoire to more-complex tasks, such as inserting pegs in holes or hammering. However, none of these actions truly demonstrated fine or in-hand manipulation capabilities, and they were commonly performed using simple two-fingered grippers. To enable multipurpose fine manipulation, roboticists focused their efforts on designing humanlike hands capable of using tools. Wielding a tool in-hand became a problem of its own, and a variety of advanced algorithms were developed to facilitate stable holding of objects and provide optimality guarantees. Because optimality was difficult to achieve in a stochastic environment, from the 1990s onward researchers aimed to increase the robustness of object manipulation at all levels. These efforts initiated the design of sensors and hardware for improved control of hand–object contacts. Studies that followed were focused on robust perception for coping with object occlusion and noisy measurements, as well as on adaptive control approaches to infer an object’s physical properties, so as to handle objects whose properties are unknown or change as a result of manipulation. ADVANCES Roboticists are still working to develop robots capable of sorting and packaging objects, chopping vegetables, and folding clothes in unstructured and dynamic environments. Robots used for modern manufacturing have accomplished some of these tasks in structured settings that still require fences between the robots and human operators to ensure safety. Ideally, robots should be able to work side by side with humans, offering their strength to carry heavy loads while presenting no danger. Over the past decade, robots have gained new levels of dexterity. This enhancement is due to breakthroughs in mechanics with sensors for perceiving touch along a robot’s body and new mechanics for soft actuation to offer natural compliance. Most notably, this development leverages the immense progress in machine learning to encapsulate models of uncertainty and support further advances in adaptive and robust control. Learning to manipulate in real-world settings is costly in terms of both time and hardware. To further elaborate on data-driven methods but avoid generating examples with real, physical systems, many researchers use simulation environments. Still, grasping and dexterous manipulation require a level of reality that existing simulators are not yet able to deliver—for example, in the case of modeling contacts for soft and deformable objects. Two roads are hence pursued: The first draws inspiration from the way humans acquire interaction skills and prompts robots to learn skills from observing humans performing complex manipulation. This allows robots to acquire manipulation capabilities in only a few trials. However, generalizing the acquired knowledge to apply to actions that differ from those previously demonstrated remains difficult. The second road constructs databases of real object manipulation, with the goal to better inform the simulators and generate examples that are as realistic as possible. Yet achieving realistic simulation of friction, material deformation, and other physical properties may not be possible anytime soon, and real experimental evaluation will be unavoidable for learning to manipulate highly deformable objects. OUTLOOK Despite many years of software and hardware development, achieving dexterous manipulation capabilities in robots remains an open problem—albeit an interesting one, given that it necessitates improved understanding of human grasping and manipulation techniques. We build robots to automate tasks but also to provide tools for humans to easily perform repetitive and dangerous tasks while avoiding harm. Achieving robust and flexible collaboration between humans and robots is hence the next major challenge. Fences that currently separate humans from robots will gradually disappear, and robots will start manipulating objects jointly with humans. To achieve this objective, robots must become smooth and trustable partners that interpret humans’ intentions and respond accordingly. Furthermore, robots must acquire a better understanding of how humans interact and must attain real-time adaptation capabilities. There is also a need to develop robots that are safe by design, with an emphasis on soft and lightweight structures as well as control and planning methodologies based on multisensory feedback.