Three possible settings are considered for the question of two interacting charged conducting balls: (1) both balls are kept at constant and equal potentials; (2) one ball is charged and isolated, the other is kept at a constant potential with the same sign as the first, and (3) both balls are like charged and isolated. It is shown that fundamentally different problems generally arise here: whereas in the first case the balls always repel, in the second and third cases fairly wide ranges of radius and charge ratios can always be found in which the balls attract each other at close distances. These ranges are identified in the paper. The results are presented of experiments that demonstrate both the repulsion and attraction of like-charged balls. Theory and experiment show satisfactory agreement, both qualitatively and quantitatively.