In this minireview we have attempted to provide some overall perspective on the question of how various forms of diffusion in reduced dimensions, or diffusion within a nonspecifically bound state, can speed biological interactions beyond the limits normally set by three-dimensional diffusion processes. To this end we began by discussing the rates expected for small molecules engaged in classical elastic collisions. We then proceeded to modify this picture by introducing first the features of inelastic macromolecular collisions in solution, then the effects of specific electrostatic fields set up around macromolecules of known structure at low ionic strengths, and finally the special rate enhancements available to DNA-protein interactions because of the particular geometry of the DNA molecule and the multiple conformations that can be assumed by the protein component. We hope that this exposition will help to clarify the subject for others and also will stimulate more focused examination of this type of problem, both in DNA-protein interaction systems and in other biological systems where such rate facilitation might apply.