As robots move from controlled environments into real-world settings, it becomes increasingly crucial to ensure that they perform as expected. A key step toward that goal is a rigorous specification of the desired robot behavior, capturing intricate temporal, spatial, and logical requirements. Complementing this, plan and control synthesis methods are needed to fulfill these specifications with provable guarantees. This manuscript presents temporal logics - particularly linear and signal temporal logic - as expressive specification languages for robot behavior over time. We then discuss principles of formal synthesis, from discrete graph- and game-based approaches to sampling-based motion planning, trajectory optimization, and control-certificate-based synthesis. Finally, we outline challenges in deploying formal synthesis in real-world robotics, emphasizing the interplay between modeling fidelity, computational tractability, and the types of rigorous guarantees that can be achieved.

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