Mobile robots are complex systems that combine mechanical elements such as wheels and gears, electromechanical devices such as motors, clutches and brakes, digital circuits such as processors and smart sensors, and software programs such as embedded controllers. They have mechanical constraints (e.g., a car-like robot cannot move sideways), limited energy resources, and computation, sensing, and communication capabilities. They operate in environments cluttered with possibly moving and shape changing obstacles, and their objectives can change over time, such as in the case of appearing and disappearing targets. Robot motion planning and control is the problem of automatic construction of robot control strategies from task specifications given in high-level, human-like language. The challenge in this area is the development of computationally efficient frameworks allowing for systematic, provably correct, control design accommodating both the robot constraints and the complexity of the environment, while at the same time allowing for expressive task specifications.