Today, our urban centres are an embodiment of the complex, historical co-evolution of knowledge, desires and technology. Our activities co-evolve with our aspirations, mediated by the existing technologies and social structures. The city represents the accretion and accumulation of successive layers of collective activity, structuring and being structured by other, increasingly distant cities, reaching now right around the globe. This historical and structural evolution cannot therefore be understood or captured by any set of fixed mathematical relations such as simultaneous, or even dynamic, equations. Structural changes imply that the patterns of growth, and their underlying reasons change over time, and therefore that any model attempting to represent changing urban morphology and patterns of flow, must be dynamic, based on the mechanisms that drive the changes occurring at a given moment. This carefully edited post-proceedings volume gathers a snapshot view, by leading researchers in field, of current complexity theories of cities. In it, the achievements, criticisms and potentials yet to be realized are reviewed and the implications to planning and urban design are assessed.