The review discusses some consequences of the widespread partial uncoupling of the reproduction of organelle DNA from that of nuclear DNA. I propose that in certain circumstances natural selection favors intraorganismal reproductive competition between different varieties of organelle DNA, and in other circumstances selection favors competition between organelle and nuclear DNA. Evidence is marshalled to show that such competition occurs in nature. Situations which would lead to selection for both kinds of competition are described and are shown to be relatively common. A number of examples of apparent competition of predicted kinds are presented. Several testable predictions are made from the theory, and it is shown that the available data are in accord with them. Similar kinds of reproductive competition are predicted to occur in some other symbiotic relationships, and possible examples are presented for two of them: bacterial plasmids and endozoic algae.