Evolutionary Transitions: how do levels of complexity emerge?

It is a common observation that complex systems have a nested or hierarchical structure: they consist of subsystems, which themselves consist of subsystems, and so on, until the simplest components we know, elementary particles. It is also generally accepted that the simpler, smaller components appeared before the more complex, composite systems. Thus, evolution tends to produce more complex systems, gradually adding more levels to the hierarchy. For example, elementary particles evolved subsequently into atoms, molecules, cells, multicellular organisms, and societies of organisms. These discrete steps, characterized by the emergence of a higher level of complexity, may be called "evolutionary transitions". The logic behind this sequential complexification appears obvious: you can only build a higher order system from simpler systems after these building blocks have evolved themselves. The issue becomes more complicated when you start looking for the precise mechanisms behind these evolutionary transitions, and try to understand which levels have appeared at what moment, and why.