Progress in the theory of electrostatic interactions between charged particles.

In this perspective we examine recent theoretical developments in methods for calculating the electrostatic properties of charged particles of dielectric materials. Particular attention is paid to the phenomenon of like-charge attraction and we investigate the specific conditions under which particles carrying the same sign of charge can experience an attractive interaction. Given favourable circumstances, it is shown that even weakly polarisable materials, such as oil droplets and polymer particles, can experience like-charge attraction. Emphasis is also placed on the numerical accuracy of the multipole approach adopted in many electrostatic solutions and on the importance of establishing strict convergence criteria when addressing problems involving particulate materials with high dielectric constants.