Evolutionary theory is formulated in terms of individuals that carry heritable information and are subject to selective pressures. However, individuality itself is a trait that had to evolve - an individual is not an indivisible entity, but a result of evolutionary processes that necessarily begin at the lower level of hierarchical organisation. Traditional approaches to biological individuality focus on cooperation and relatedness within a group, division of labour, policing mechanisms and strong selection at the higher level. Nevertheless, despite considerable theoretical progress in these areas, a full dynamical first-principles account of how new types of individuals arise is missing. To the extent that individuality is an emergent trait, the problem can be approached by recognising the importance of individuating mechanisms that are present from the very beginning of the transition, when only lower-level selection is acting. Here we review some of the most influential theoretical work on the role of individuating mechanisms in these transitions, and demonstrate how a lower-level, bottom-up evolutionary framework can be used to understand biological complexity involved in the origin of cellular life, early eukaryotic evolution, sexual life cycles and multicellular development. Some of these mechanisms inevitably stem from environmental constraints, population structure and ancestral life cycles. Others are unique to specific transitions - features of the natural history and biochemistry that are co-opted into conflict mediation. Identifying mechanisms of individuation that provide a coarse-grained description of the system's evolutionary dynamics is an important step towards understanding how biological complexity and hierarchical organisation evolves. In this way, individuality can be reconceptualised as an approximate model that with varying degrees of precision applies to a wide range of biological systems.