| We study the problem of grasping an unknown object with constant cross section using various "reactive" robot hands. In the simplest example, we equip a standard parallel-jaw gripper with several light-beam sensors (close to each jaw) and implement a reactive algorithm for grasping polygonal objects with this architecture. Extending these ideas further, we also devise two- and three-fingered reactive hands for objects with smooth boundary and equip these with distance and angle sensors that are located at the finger tips. The sensors used are simple and provide only limited and immediate information, but they allow us to reactively find a good grasp on an object of unknown geometry and dynamics. When grasped, the forces applied will be normal to the object boundary. Furthermore, in all cases, the object is not disturbed as the grasping points are being sought.