Here Give some recent studies on iterative methods for solving linear systems arising from many applications, specially preconditioned iterative methods for saddle point problems. The main point is to transform the indefinite systems to symmetric and positive definite well-conditioned systems such that we can apply the conjugate gradient method to solve the problems. Also some no-orthogonal iterative method, semi-conjugate direction method was introduced to solve general nonsymmetric systems. Finally some open problems are presented for future research.