We summarize progress in studying a model of two Kondo impurities interacting directly with a conduction electron sea and indirectly with each other. In the presence of particle-hole symmetry, a critical point exists at finite ratio of (antiferromagnetic) RKKY coupling to Kondo temperature. For the more general case of no particle-hole symmetry, however, indications from both a 1 N (mean field) expansion and numerical renormalization group studies of potential scattering are that the transition is washed out. We discuss the implications of these findings on pair correlations in a real (lattice) system. © 1991.