We attempt a comprehensive review of all published research in nondestructive evaluation (NDE) performed with the superconducting quantum interference device (SQUID) magnetometer since the first work was reported in the mid-1980s. The SQUID is the most sensitive detector of magnetic flux known. The energy sensitivity of the SQUID may make it the most sensitive detector of any kind. The research on SQUIDs for NDE is based on the promise of that sensitivity and on the various other desirable properties developed for SQUID instrumentation in biomagnetism and other fields. The sensitivity of SQUID instruments down to very low frequencies allows them to function as eddy-current sensors with unparalleled depth resolution, and to image the static magnetization of paramagnetic materials and the flow of near-dc corrosion currents. The wide dynamic range of the SQUID makes it possible to image defects in steel structures and to measure the magnetomechanical behaviour of ferromagnetic materials with high sensitivity. In the last decade SQUID instrumentation designed specifically for NDE has appeared and improved the spatial resolution of most work to roughly 1 mm, with promise of another order of magnitude improvement within the next five years. Algorithms for flaw detection and image deconvolution have begun to flourish. With many talented, industrious people in the field, the future of SQUID NDE looks bright, provided the crucial first niche can be found.