Virtual fixtures are control modes implemented in software that assist the user in a specific task. This dissertation extends the concept of constraint-based virtual fixtures to dexterous tasks. We use motion constraints to generate either guidance or forbidden virtual fixtures. The first topic addressed in this dissertation is the motion control of a robot using a library of primitive constraints. We address the issue of combining these primitives to formulate complex task behaviors for the robot. We also extend the constraint control algorithm to two or more robots. The multiple robot constraint control allows complex spatial and temporal relationships to be maintained between robots. Next, two applications of motion constraints, illustrating their ability to assist in realistic surgical tasks, are presented. The first task is manipulating a curved needle to pass it between tissues to be sutured. The primary challenge in this task is the manipulation of a curved needle under non-ideal haptic conditions using a robot with complex kinematics. The second task is manipulating a half-square knot to position it at a target point. This bimanual task demonstrates our algorithm's ability to handle complex spatial and temporal relations between two or more arms. Finally, a telerobotic system consisting of daVinci Master Tele-Manipulators (MTM), two novel S-DoF hybrid manipulators (JHU-Snake), and stereo visualization is presented. Our contribution was the overall system integration and development of the teleoperator control for the JHU-Snake. The teleoperator control method uses two weighted, multi-objective constrained least square (LS) optimization problems—one for the master controller and the other for the slave controller. The optimization problem for the slave absolves the user from managing the dexterity of the snake-like units along with other joints of JHU-Snake robot while satisfying physical limits imposed by miniaturization of robot actuators. Though the teleoperator control is particularly relevant to the JHU-Snake, it is also applicable to a broad range of redundant dexterous robots. The dissertation concludes with some interesting extensions and improvements that could build on the results presented.