The traditional view of quantum mechanics as restricting what can be done classically has been turned upside down by quantum information science, which explores how coherent quantum-mechanical information processing can be used to accomplish tasks that would be impossible in a classical world. Implementing quantum information processing protocols promises to be one of the enduring scientific and technological challenges of the 21st Century. I will focus on quantum computation: why it’s important, what is required to make it work, and how it might be implemented in physical systems.