What is biological complexity? How many sorts exist? Are there levels of complexity? How are they related to one another? How is complexity related to the emergence of new phenotypes? To try to get to grips with these questions, we consider the archetype of a complex biological system, Escherichia coli. We take the position that E. coli has been selected to survive adverse conditions and to grow in favourable ones and that many other complex systems undergo similar selection. We invoke the concept of hyperstructures which constitute a level of organisation intermediate between macromolecules and cells. We also invoke a new concept, competitive coherence, to describe how phenotypes are created by a competition between maintaining a consistent story over time and creating a response that is coherent with respect to both internal and external conditions. We suggest how these concepts lead to parameters suitable for describing the rich form of complexity termed hypercomplexity and we propose a relationship between competitive coherence and emergence.