Preconditioned iterative methods for symmetric eigenvalue problems are finally becoming a numerical standard for extremely large problems. In this talk, we present a survey of some results, mostly theoretical convergence rate estimates, for such methods. We consider preconditioned analogs of the power method, the steepest descent/ascent method, the Lanczos-type methods by Scott and Davidson, the conjugate gradient methods. We discuss possible approaches for deriving formulas of the methods and conclude that different approaches lead to the same methods.