Several dynamical methods used in predictability studies for numerical weather forecasting and climate prediction are briefly introduced. For the first type, the methods of linear singular vector (LSV), conditional nonlinear optimal initial perturbation (CNOP-I), Lyapunov exponent, and nonlinear local Lyapunov exponent (NLLE) are reviewed. The LSV and CNOP-I have been used to estimate maximal forecast errors and to identify sensitive areas in the initial stages of weather and climate prediction. Because the former method is based on a linear model and has limitations in determining nonlinear atmospheric and oceanic motions, the latter is recommended for use in nonlinear models. The Lyapunov exponent and NLLE have been used to study predictable time issues. The former is based on linear models; therefore, it cannot be used to explore nonlinear effects. However, the latter considers these effects and can be used to more accurately estimate maximal predictable time in actual weather and climate prediction. For the second type of predictability study, this paper reviews only the method of conditional nonlinear optimal parameter perturbation (CNOP-P). The CNOP-P can be used to search parameter perturbations that largely affect the forecasts and to determine those that should be verified by observation. A comparison of forecast errors brought by CNOP-I and CNOP-P can be used to determine whether the model or initial state should first be improved.