The significant advances made in the design and construction of anthropomorphic robot hands, endow them with prehensile abilities reaching that of humans. However, using these powerful hands with the same level of expertise that humans display is a big challenge for robots. Traditional approaches use finger-tip (precision) or enveloping (power) methods to generate the best force closure grasps. However, this ignores the variety of prehensile postures available to the hand and also the larger context of arm action. This thesis explores a paradigm for grasp formation based on generating oppositional pressure within the hand, which has been proposed as a functional basis for grasping in humans (MacKenzie and Iberall, 1994). A set of opposition primitives encapsulates the hand's ability to generate oppositional forces. The oppositional intention encoded in a primitive serves as a guide to match the hand to the object, quantify its functional ability and relate this to the arm. In this thesis we leverage the properties of opposition primitives to both interpret grasps formed by humans and to construct grasps for a robot considering the larger context of arm action. In the first part of the thesis we examine the hypothesis that hand representation schemes based on opposition are correlated with hand function. We propose hand-parameters describing oppositional intention and compare these with commonly used methods such as joint angles, joint synergies and shape features. We expect that opposition-based parameterizations, which take an interaction-based perspective of a grasp, are able to discriminate between grasps that are similar in shape but different in functional intent. We test this hypothesis using qualitative assessment of precision and power capabilities found in existing grasp taxonomies. The next part of the thesis presents a general method to recognize oppositional intention manifested in human grasp demonstrations. A data glove instrumented with tactile sensors is used to provide the raw information regarding hand configuration and interaction force. For a grasp combining several cooperating oppositional intentions, hand surfaces can be simultaneously involved in multiple oppositional roles. We characterize the low-level interactions between different surfaces of the hand based on captured interaction force and reconstructed hand surface geometry. This is subsequently used to separate out and prioritize multiple and possibly overlapping oppositional intentions present in the demonstrated grasp. We evaluate our method on several human subjects across a wide range of hand functions. The last part of the thesis applies the properties encoded in opposition primitives to optimize task performance of the arm, for tasks where the arm assumes the dominant role. For these tasks, choosing the strongest power grasp available (from a force-closure sense) may constrain the arm to a sub-optimal configuration. Weaker grasp components impose fewer constraints on the hand, and can therefore explore a wider region of the object relative pose space. We take advantage of this to find the good arm configurations from a task perspective. The final hand-arm configuration is obtained by trading of overall robustness in the grasp with ability of the arm to perform the task. We validate our approach, using the tasks of cutting, hammering, screw-driving and opening a bottle-cap, for both human and robotic hand-arm systems.