Self-promoting elements (also called ultraselfish genes, selfish genes, or selfish genetic elements) are vertically transmitted genetic entities that manipulate their "host" so as to promote their own spread, usually at a cost to other genes within the genome. Examples of such elements include meiotic drive genes and cytoplasmic sex ratio distorters. The spread of a self-promoting element creates the context for the spread of a suppressor acting within the same genome. We may thus say that a genetic conflict exists between different components of the same genome. Here we investigate the properties of such conflicts. First we consider the potential diversity of genomic conflicts and show that every genetic system has potential conflicts. This is followed by analysis of the logic of conflicts. Just as Evolutionarily Stable Strategy (ESS) terminology provides a short cut for discussion of much in behavioral ecology, so the language of modifier analysis provides a useful terminology on which to base discussions of conflicts. After defining genetic conflict, we provide a general analysis of the conflicting parties, and note a distinction between competing and conflicting genes. We then provide a taxonomy of possible short- and long-term outcomes of conflicts, noting that potential conflict in an unconstrained system can never be removed, and that the course of evolution owing to conflict is often unpredictable. The latter is most particularly true for strong conflicts in which suppressors may take surprising forms. The possibility of extended conflicts in the form of "arms races" between element and suppressor is illustrated. The peculiar redundancy of these systems is one possible trace of conflict, and others are discussed. That homologous conflicts may find highly different expression is discussed by referring to the mechanistic differences that are thought to underlie the action of the two best-described meiotic drive genes, and by the multiplicity of forms of cytoplasmic sex ratio distorters. The theoretical analysis establishes a logical basis for thinking about conflicts, but fails to establish the importance of conflict in evolution. We illustrate this contentious issue through consideration of some phenomena for whose evolution conflict has been proposed as an important force: the evolution of sex, sex determination, species, recombination, and uniparental inheritance of cytoplasmic genes. In general, it is proposed that conflict may be a central force in the evolution of genetic systems. We conclude that an analysis of conflict and its general importance in evolution is greatly aided by application of the concept of genetic power. We consider the possible components of genetic power and ask whether and how power evolves.