This thesis focuses on task-space control of kinematically redundant robot manipulators with telerobotic applications. The first aim is to design asymptotically stable sub-task controllers for kinematically redundant robot manipulators subject to parametric uncertainties in their dynamics. Initially, a novel combined analysis of the task-space tracking and sub-task controllers is performed for redundant robots having only one extra degree of freedom. Next, an extended task-space controller is designed by integrating manipulator Jacobian with the sub-task Jacobian. Both controllers ensure task-space tracking and sub-task objectives at the amount of redundant degree of freedom. As the second aim, two robust control methods are proposed for task-space tracking of robot manipulators. First, a novel continuous robust controller is designed despite dynamic model and Jacobian uncertainties to ensure asymptotic task-space tracking while requiring measurements of joint positions and velocities. Then, a robust output feedback controller is proposed to ensure ultimately bounded task-space tracking requiring neither measurements of joint positions or velocities nor accurate knowledge of kinematic and dynamic models. The third aim is to develop a passive decomposition method for task-space control of bilateral teleoperation systems. The proposed method ensures coordination of master and slave robots while achieving a desired overall motion for the bilateral teleoperation system. The proposed method is firstly considered for teleoperation systems consisting of kinematically similar master and slave robots, then extended to be applicable to kinematically redundant teleoperation systems. Simulation and experimental studies are performed to present the viability of the proposed methods.