The basic problem in an evolutionary transition is to understand how a group of individuals becomes a new kind of individual, possessing the property of heritable variation in fitness at the new level of organization. During an evolutionary transition, for example, from single cells to multicellular organisms, the new higher-level evolutionary unit (multicellular organism) gains its emergent properties by virtue of the interactions among lower-level units (cells). We see the formation of cooperative interactions among lower-level units 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 new levels of fitness, it creates the opportunity for conflict between levels as deleterious mutants arise and spread within the group. Fundamental to the emergence of a new higher-level unit is the mediation of conflict among lower-level units in favor of the higher-level unit. The acquisition of heritable variation in fitness at the new level, via conflict mediation, requires the reorganization of the basic components of fitness (survival and reproduction) and life-properties (such as immortality and totipotency) as well as the co-option of lower-level processes for new functions at the higher level. The way in which the conflicts associated with the transition in individuality have been mediated, and fitness and general life-traits have been re-organized, can influence the potential for further evolution (i.e., evolvability) of the newly emerged evolutionary individual. We use the volvocalean green algal group as a model-system to understand evolutionary transitions in individuality and to apply and test the theoretical principles presented above. Lastly, we discuss how the different notions of individuality stem from the basic properties of fitness in a multilevel selection context.