Teleoperation allows a human to control a robot to perform dexterous tasks in remote, dangerous, or unreachable environments. A perfect teleoperation system would enable the operator to complete such tasks at least as easily as if he or she was to complete them by hand. This ideal teleoperator must be perceptually transparent, meaning that the interface appears to be nearly nonexistent to the operator, allowing him or her to focus solely on the task environment, rather than on the teleoperation system itself. Furthermore, the ideal teleoperation system must give the operator a high sense of presence, meaning that the operator feels as though he or she is physically immersed in the remote task environment. This dissertation seeks to improve the transparency and presence of robot-arm-based teleoperation systems through a human-centered design approach, specifically by leveraging scientific knowledge about the human motor and sensory systems. First, this dissertation aims to improve the forward (efferent) teleoperation control channel, which carries information from the human operator to the robot. The traditional method of calculating the desired position of the robot's hand simply scales the measured position of the human's hand. This commonly used motion mapping erroneously assumes that the human's produced motion identically matches his or her intended movement. Given that humans make systematic directional errors when moving the hand under conditions similar to those imposed by teleoperation, I propose a new paradigm of data-driven human-robot motion mappings for teleoperation. The mappings are determined by having the human operator mimic the target robot as it autonomously moves its arm through a variety of trajectories in the horizontal plane. Three data-driven motion mapping models are described and evaluated for their ability to correct for the systematic motion errors made in the mimicking task. Individually-fit and population-fit versions of the most promising motion mapping model are then tested in a teleoperation system that allows the operator to control a virtual robot. Results of a user study involving nine subjects indicate that the newly developed motion mapping model significantly increases the transparency of the teleoperation system. Second, this dissertation seeks to improve the feedback (afferent) teleoperation control channel, which carries information from the robot to the human operator. We aim to improve a teleoperation system a teleoperation system by providing the operator with multiple novel modalities of haptic (touch-based) feedback. We describe the design and control of a wearable haptic device that provides kinesthetic grip-force feedback through a geared DC motor and tactile fingertip-contact-and-pressure and high-frequency acceleration feedback through a pair of voice-coil actuators mounted at the tips of the thumb and index finger. Each included haptic feedback modality is known to be fundamental to direct task completion and can be implemented without great cost or complexity. A user study involving thirty subjects investigated how these three modalities of haptic feedback affect an operator's ability to control a real remote robot in a teleoperated pick-and-place task. This study's results strongly support the utility of grip-force and high-frequency acceleration feedback in teleoperation systems and show more mixed effects of fingertip-contact-and-pressure feedback.