Picking up a cup requires transporting the arm to the cup (transport component) and preshaping the hand appropriately to grasp the handle (grip component). Here, we used functional magnetic resonance imaging to examine the human neural substrates of the transport component and its relationship with the grip component. Participants were shown three-dimensional objects placed either at a near location, adjacent to the hand, or at a far location, within reach but not adjacent to the hand. Participants performed three tasks at each location as follows: (1) touching the object with the knuckles of the right hand; (2) grasping the object with the right hand; or (3) passively viewing the object. The transport component was manipulated by positioning the object in the far versus the near location. The grip component was manipulated by asking participants to grasp the object versus touching it. For the first time, we have identified the neural substrates of the transport component, which include the superior parieto-occipital cortex and the rostral superior parietal lobule. Consistent with past studies, we found specialization for the grip component in bilateral anterior intraparietal sulcus and left ventral premotor cortex; now, however, we also find activity for the grasp even when no transport is involved. In addition to finding areas specialized for the transport and grip components in parietal cortex, we found an integration of the two components in dorsal premotor cortex and supplementary motor areas, two regions that may be important for the coordination of reach and grasp.