This review is of current and projected applications of optical fibers to observational astronomy. The intent is to provide astronomers with a broad perspective on the subject, with the hope of encouraging productive use of optical fibers in the design of new instrumentation. The unique characteristics of fibers have been (or soon will be) exploited to advantage in several areas of astronomical instrumentation, including multiplexers for muti-object spectrographs, remote optical feeds for spectrographs and photometers, coherent beam recombiners for optical interferomety, and many miscellaneous applications. We discuss the most important such applications in detail, with reference to operational instruments wherever possible, and with emphasis on the optical properties of fibers and the engineering considerations encountered in their application to observational astronomy.