This chapter discusses methods for efficiently solving Poisson and eigenvalue problems on grids in real space using multigrid techniques. The purpose of the chapter is to provide an introduction to developing useful solvers for electrostatics and electronic structure problems. High order finite difference approximations are used in the discretization, leading to structured sparse matrix representations of the equations. The fully numerical solution is then obtained iteratively on a sequence of grids of increasing resolution. Preconditioning from the coarser levels and the multigrid correction cycles on the finer scales lead to rapid convergence of the desired functions. Typically, the solution is obtained to within the truncation errors due to discretization in roughly ten relaxation sweeps on the finest level. ©2000 American Institute of Physics.