Our homes, offices and urban surroundings are carefully built to be inhabited by us, humans. Tools and furniture are designed to be easily manipulated by the human hand. Floors and stairs are modeled for human-sized legs. For robots to work seamlessly in our environments they should have bodies that resemble in shape, size and strength to the human body, and use these with the same dexterity and reactivity. This talk will provide an overview of techniques developed at LASA to enable robust, fast and flexible manipulation. Learning is guided by human demonstrations. Robust manipulation is achieved through sampling over distributions of feasible grasps. Smooth exploration leverages on complete tactile sensing coverage and learned variable impedance strategies. Bi-manual coordination offers ways to exploit the entire robot's workspace. Imprecise positioning and sensing is overcome using active compliant strategies, similar to that displayed by humans when facing situations with high uncertainty. The talk will conclude with examples in which robots achieve super-human capabilities for catching fast moving objects with a dexterity that exceeds that displayed by human beings.