Started with a purely theoretical paper by Samokish in 1958 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, as well as their block variants. We discuss possible approaches for deriving formulas of the methods and conclude that different approaches lead to the same methods. We argue against a popular choice of constructing a preconditioner for the shifted matrix that appeared in the Rayleigh Quotient Method.