The objective of the proposed research is to realize agile behaviors coupled with safe and reliable reactions to the environment for robot locomotion and manipulation. The challenge is predominantly rooted in two distinct requirements: the need for efficient trajectory planning for complex dynamical systems and the imperative for safe and responsive task planning that adheres to physical feasibility. In this dissertation, novel approaches grounded in distributed optimization are proposed, tailored to legged locomotion and soft-contact manipulation problems with meticulous consideration of whole-body dynamics and constraint decomposition. The second challenge of task planning originates from the mismatch between the robot's abstract-level decisions and its physical-level capabilities. In the realm of legged locomotion, Linear Temporal Logic (LTL)-based reactive synthesis is adopted in this dissertation to abstract the dynamic contact planning problem as a high-level gait design and decision-making problem.