This review is concerned with the physical problems of fiber ring interferometry which underlies the fiber-optic gyroscopy harnessing the Sagnac effect. Locally reciprocal and locally nonreciprocal physical effects are considered, including polarization, transient, magnetic, nonlinear, and relativistic effects. These effects are responsible for the appearance of additional signals, which are similar to the rotation signal, at the output of a fiber-optic gyroscope. The causes of instability of the effects leading to the drift of the output signal are analyzed. The sources of fluctuations which limit the ultimate sensitivity of fiber gyroscopes are considered. We discuss different fields of application of fiber ring interferometers and fiber gyroscopes built around them for practical purposes and to basic research. The prospects for further development of fiber gyroscopy are considered.
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