Grasping an object is a matter of first moving a prehensile organ at some position in the world, and then managing the contact relationship between the prehensile organ and the object. Once the contact relationship has been established and made stable, the object is part of the body and it can move in the world. As any action, the action of grasping is ontologically anchored in the physical space while the correlative movement originates in the space of the body. Evolution has found amazing solutions that allow organisms to rapidly and efficiently manage the relationship between their body and the world. It is then natural that roboticists consider taking inspiration of these natural solutions, while contributing to better understand their origin.