Due to the manufacturing error and in-service degradation of gas turbines, there is always a deviation between the actual geometry and the design geometry. This geometric deviation has a prominent uncertainty characteristic, resulting in a dispersion of the gas turbine performance and thereby reducing the manufacturing qualification rate and service life. As the performance and reliability requirements of gas turbines increase continually, more and more attention has been paid to the quantitative study of the effect of the geometric uncertainty on performance. In this paper, the main sources and features of gas turbine geometric uncertainty are reviewed first. Then, the basic principles, characteristics, and application in gas turbines of different uncertainty quantification (UQ) methods are reviewed. Finally, the progress, challenges, and prospects for correlational research are summarized in the conclusion.