Quantum computing has great potential advantages over classical computation in solving certain types of problems. A particularly significant example has been provided by Shor, who demonstrated that a quantum computer could, at least in principle, provide an enormous advantage in factoring very large numbers. Although the potential advantages of quantum computation are great, so are the challenges in the path towards the development of a practical quantum computer. This presentation will review the fundamental requirements of a quantum computing system, and the principles involved in the most important potential applications so far identified. The presentation will focus on what is, arguably, the most promising approach towards practical quantum computing: magnetic resonance.