Superconducting detector arrays have become the standard technology for the current generation of millimeterwave and submm-wave astronomical instruments on individual (single dish) telescopes. Superconducting heterodyne arrays are used for spectroscopic surveys and direct detector arrays are used for photometric imaging and low resolution spectroscopy. Most of these direct detector arrays consist of bolometers with superconducting thermometers called Transition Edge Sensors (TES) and are read out with multiplexed superconducting quantum interference device (SQUID) current amplifiers. Another superconducting detector technology called Kinetic Inductance Detectors (KIDs) is starting to be used in new astronomical instruments as well. This review describes the properties of these two types of detectors and the prospects for future development of both types of technologies toward larger pixel counts and more capable instruments.