Surface charging or polarization can strongly affect the nature of interactions between charged dielectric objects, particularly when sharp dielectric discontinuities are involved. By relying on a generalized image method, we derive an analytical, perturbative theory of the polarization and the interactions between charged particles in many-body systems. The validity and accuracy of the theory are established by comparing its predictions to full-blown numerical solutions. The importance of polarizability is then demonstrated for clusters of dielectric spheres, as well as a periodic crystal of charged dielectric spheres arranged into a NaCl-type lattice. The analytical framework for understanding the consequences of polarization will enable molecular simulations of large systems of polarizable particles. (C) 2016 Elsevier Inc. All rights reserved.