The basic problem in an evolutionary transition in complexity is to understand how a group of individuals becomes a new kind of individual, having heritable variation in fitness at the new level of organization. We see the formation of cooperative interactions among lower-level individuals as a necessary step in evolutionary transitions; only cooperation transfers fitness from lower levels (costs to group members) to higher levels (benefits to the group). As cooperation creates a new level of fitness, it creates the opportunity for conflict between the new level and the lower level. Fundamental to the emergence of a new higherlevel individual is the mediation of conflict among lower-level individuals in favor of the higher-level unit. We define a conflict mediator as a feature of the cell-group (the emerging multicellular organism) that restricts the opportunity for fitness variation at the lower level (cells) and/or enhances the variation in fitness at the higher level (the cell-group). There is abundant evidence that organisms are endowed with just such traits and numerous examples are reviewed here from the point of view of a population genetic model of conflict mediation. Our model considers the evolution of genetic modifiers that mediate conflict between the cell and the cell-group. These modifiers alter the parameters of development, or rules of formation, of cell-groups. By sculpting the fitness variation and opportunity for selection at the two levels, conflict modifiers create new functions at the organism level. An organism is more than a group of cooperating cells related by common descent and requires adaptations that regulate conflict within itself. Otherwise their individuality and continued evolvability is frustrated by the creation of withinorganism variation and conflict between levels of selection. Conflict leads to greater individuality and harmony for the organism, through the evolution of adaptations that reduce it.