Iterative methods for solving linear systems of equations compute, starting from an initial vector, a sequence of approximate solutions with the goal that this sequence converges to the solution of the system. In this chapter, we will first define the concept of an iterative method and then introduce the classical splitting methods. For these methods, we will analyze the relationship between convergence and the spectral radius of the so-called iteration matrix and, based on this, derive convergence criteria. Furthermore, we will take a look at the multigrid method and examine its properties by considering the Fourier modes. The main focus of this chapter is on modern Krylov subspace methods. Here, we will first introduce the conjugate gradient method as a modification of the method of steepest descent. Finally, we turn to the GMRES method and numerous other methods such as BiCG, CGS, BiCGSTAB, TFQMR, and QMRCGSTAB.