What are the algorithmic principles that would allow a robot to run through a rocky terrain, lift a couch while reaching for an object that rolled under it or manipulate a screwdriver while balancing on top of a ladder? Our research tries to answer this seemingly naive question, which in fact resorts to understanding the fundamental principles of robotic locomotion and manipulation. One important aspect of our work focuses on the optimal exploitation of contact interactions between the robot and its environment to create more robust and efficient behaviors in uncertain and constantly changing environments. In particular, we will show recent results on legged robot control, where we use optimization techniques for real-time control of both contact interactions and robot motion. We will show experimental results on a torque controlled humanoid robot and recent trajectory optimization techniques to efficiently plan motion together with interaction forces during locomotion. The second part of the talk will focus on compliant manipulation. We developed complete systems capable of achieving complex autonomous manipulation tasks and we will show how the use of multimodal sensory information can be exploited to create very reactive behaviors and to learn contact interactions using machine learning techniques.