We describe the development of graphics processor (GPU) accelerated iterative methods and preconditioners for solving linear systems arising in science and engineering applications. Krylov subspace methods including GMRES and TFQMR have been implemented on the GPU using Nvidia Cuda. The performance of these algorithms is intimately related to the performance of matrix-vector multiplies and sparse-matrix storage formats. The convergence of an iterative solver is most often determined by the preconditioner employed. The data-parallel architecture of the GPU computing platform must be considered when selecting a preconditioner. We also report on the development of a set of preconditioners, working together with GPU accelerated iterative solvers, to provide significant acceleration. These include, but are not limited to, block Jacobi, algebraic multigrid (AMG) with novel smoothing techniques, sparse approximate inverses and CPU based ILU(k) preconditioners that work with GPU solvers.