We report a study on the optical forces between a pair of dielectric particles, based on quantum electrodynamics. At a fundamental level these forces result from a stimulated scattering process which entails a virtual photon relay between the two particles. Results for a variety of systems are secured from a completely general analysis that accommodates a system with arbitrary dielectric properties (with regard to shape, frequency response etc.) in an optical field of arbitrary complexity. Specific results are obtained and exhibited for: (a) optical forces between nanoparticles, and specifically between carbon nanotubes; (b) the effects of optical ordering, clustering and trapping associated with twisted (Laguerre-Gaussian) laser beams.