Metals are infinitely recyclable in principle, but in practice, recycling is often inefficient or essentially nonexistent because of limits imposed by social behavior, product design, recycling technologies, and the thermodynamics of separation. We review these topics, distinguishing among common, specialty, and precious metals. The most beneficial actions that could improve recycling rates are increased collection rates of discarded products, improved design for recycling, and the enhanced deployment of modern recycling methodology. As a global society, we are currently far away from a closed-loop material system. Much improvement is possible, but limitations of many kinds--not all of them technological--will preclude complete closure of the materials cycle.