Motivation is given for the development of dynamic and stochastic models of fiber optic gyros. Presented is a nonlinear system model of the fiber gyro's closed-loop optics and electronics that is simplified to a linear discrete dynamic model. Given are some of the issues arising in applying the discrete transfer function of the fiber gyro under deterministic forcing functions. The model is extended to include the gyro's output response to stochastic inputs. The resulting stochastic model includes the effects of the data acquisition system and quantization in the overall response. Discussed are techniques for evaluating the performance, both deterministic and random. Novel application of the Fourier filtering technique to simulate various types of random gyro noise, especially the mathematically pathological 1/f noise, is presented. A brief gallery of commonly applicable gyro noise is given.