People and Nature often try to optimize things; find the shortest route to the grocery store, find the most efficient way to throw a discus, cats turning themselves over efficiently, etc. Optimal control is about finding control forces to perform optimal ways of carrying out a task. Many such systems are mechanical and special techniques for computing optimal controls in mechanics will be presented. These techniques are based on recent progress in discrete mechanics. The techniques will be illustrated by systems such as falling cats, reorienting a network of satellites, optimal space mission design, systems with constraints (such as a satellite with momentum wheels), helicopter dynamics, and efficient 2D and 3D robotic walkers.