When a quantum system evolves in time or is subject to measurement, the state of the system changes according to the action of a unitary or a projection. But if we restrict our state to a subsystem, then more general types of evolutions appear to be possible, and are are mathematically described as completely positive maps. Completely positive maps are of interest to both operator algebraists and quantum information theorists, although the language used when working with them can vary between these communities. I will try to discuss them from both perspectives and will explain how Stinespringâ€™s theorem characterizes these important objects.