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The numerical solution of the N- body problem in gravitation and electrostatics has traditionally been obtained via particle-in-cell methods (PIC) since direct evaluation of all pairwise interparticle forces, requiring o(N7) operations, is too expensive. Recently, hierarchical solvers, which use data structures and lumped-force approximations, have made gridless simulations possible in O(N. log(N)) operations. In this paper, we explore the use of the fast multipole method (FMM)-a highly accurate order 0(N) algorithm- in particle simulations. W- b.e,f,-descri i the FMM f-and its relation to other methods. Technical considerations of gridless simulations such as discrete particle fluctuations, sampling errors and boundary conditions are discussed and compared with PIC methodology. Examples of electrostatic simulations in plasma physics are presented