The transistor has a number of properties that make it so useful. We discuss these and the additional properties a transistor would need to have for high performance applications at temperatures where superconductivity could contribute advantages to system-level performance. These properties then serve as criteria by which to evaluate three-terminal devices that have been proposed for applications at superconducting temperatures. FETs can retain their transistor properties at low temperatures, but their power consumption is too large for high-speed, high-density cryogenic applications. We discuss in detail why demonstrated superconducting devices with three terminals-Josephson effect based devices, injection controlled weak links, and stacked tunnel junction devices such as the superconducting transistor proposed by K. Gray and the quiteron ach fail to have true transistor-like properties. We conclude that the potentially very rewarding search for a transistor compatible with superconductivity in high performance applications must be in new directions. Copyright © 1985 by The Institute of Electrical and Electronics Engineers, Inc.