Quantum mechanics describes how matter behaves at the atomic scale and below, and is one of the most successful theories of physics that we have. One of the most surprising discoveries of the late twentieth century was that it could also give us access to a completely new (and very powerful) way of processing information: the idea of the quantum computer was born. In this talk I will introduce the basic ideas of quantum computing, its links to code-breaking and code-making, survey the current state of the art, and describe recent work at Oxford on building and using an elementary quantum network.