In recent years, significant progress has been made in the field of guaranteed computation of the bounds of eigenvalues of differential operators. By utilizing non-conforming finite element methods, the problems of guaranteed computation the eigenvalues for differential operators such as Laplace, Biharmonic, Stokes, Steklov, and Maxwell have been sequentially addressed. This report will review the fundamental theory and limitations of these methods, and introduce a high-precision guaranteed eigenvalue computation method based on the Kato-Lehmann-Goerisch theory and conforming finite element methods. It will explain how this computation method is applicable to non-uniform grids and high-order finite element methods.