The present invention is directed to the use of dielectrophoretic forces for the arbitrary manipulation of micrometer- and nanometer-sized particles and to devices capable of arbitrarily manipulating micrometer- and nanometer-sized particles by means of dielectrophoretic forces within a two- or three-dimensional region. The devices and methods of the invention are capable of arbitrarily controlling the velocities, locations, and forces applied to a particle, arbitrarily specifying a force or set of forces at a location in space, and determining friction and/or drag coefficients of a particle, and are thus well-suited for a range of applications including cell sorting, drug delivery, as a diagnostic tool for determining membrane stiffness, and in the heterogeneous integration of micro- and nano-components through directed assembly.