This article analyzes the evolution and current trends in aerial robotic manipulation, comprising helicopters, conventional underactuated multirotors, and multidirectional thrust platforms equipped with a wide variety of robotic manipulators capable of physically interacting with the environment. It also covers cooperative aerial manipulation and interconnected actuated multibody designs. The review is completed with developments in teleoperation, perception, and planning. Finally, a new generation of aerial robotic manipulators is presented with our vision of the future.