Quantum computers hold the promise to revolutionize the way we secure information, compute and understand the quantum world. Although general-purpose quantum computers appear to be a long way off, we do have good test-beds of small quantum processors. One of the most versatile quantum test-beds is nuclear magnetic resonance (NMR): a version of which is familiar to many in the guise of the medical imaging modality, MRI. In fact NMR has broad importance to society: it is used in drug discovery, in oil exploration and to monitor the processing of cheese and chocolate. We will introduce NMR, show how it helps us understand quantum computing and we will look at how concepts based on quantum computing can improve NMR applications.