In this talk, we introduce a convergence theory for general two-level methods, whose hierarchical spaces can be either overlapping or nonoverlapping. Specifically, we first give a succinct and easy-to-use identity for characterizing the convergence factor of two-level methods with Galerkin coarse solver, followed by discussions on its applications. Then, we present several convergence estimates for two-level methods with approximate coarse solvers, including both linear and nonlinear cases. Numerical examples are also provided to illustrate our theoretical results.