Contact and impact are phenomena of central importance in mechanics. In this chapter we view rigid body impact as a limiting case of impact between flexible bodies, the latter actually being a harder problem to solve but an easier problem to visualize, especially with the help of the many slow-motion videos available on the internet. Conservation of momentum provides the framework for thinking about and solving impact problems. We formulate impact problems as a time integral of the equations of motion over the very brief time of impact (which goes to zero in the limit of rigid body impact). We end the chapter with the development of a general computational framework for solving impact problems.