The use of trapped atomic ions in the field of quantum information processing is briefly reviewed. We summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We discuss the potential of trapped ions to reach fault-tolerant error levels in a large-scale system, and highlight some of the problems that will be faced in achieving this goal. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are briefly discussed.Photograph of a "surface-electrode" trap composed of 150 zones and six "Y"-type junctions, where the ion qubits are suspended approximately 40 μm above the surface. By applying time varying potentials to the electrodes, ions in different locations can be brought together to implement logic gates with laser beams that are focused onto the ions. (Trap fabrication and photograph by Jason Amini, NIST)