Contact interactions are pervasive in key real-world robotic tasks like manipulation and walking. However, the non-smooth dynamics associated with impacts and friction remain challenging to model, and motion planning and control algorithms that can fluently and efficiently reason about contact remain elusive. In this talk, I will share recent work from my research group that takes an “optimization-first” approach to these challenges: collision detection, physics, motion planning, and control are all posed as constrained optimization problems.  We then build a set of algorithmic and numerical tools that allow us to flexibly compose these optimization sub-problems to solve complex robotics problems involving discontinuous, unplanned, and uncertain contact mechanics.