Complex systems play an important role across science and technology. However, their interwoven structures and nonlinear dynamics makes analysis and control a challenge. We developed a range of mathematical measures and computational tools to help understand these systems. This was based on the formalism of an Evolving Dynamical Network (EDN) designed to coherently capture their networked structure, dynamics and evolution. Bringing these aspects together, we investigated how synchronisation of a dynamical network can be enhanced by computational evolution of the underlying structure. Unlike other methods that solely consider topological features during evolution, we allowed for simulated dynamics to guide this process. Standard network analysis of the resultant topologies illustrated many similarities between the networks, but also highlighted important differences for those evolved using simulated dynamics. We found the existence of a topological bifurcation as connection strengths were increased, and the robust emergence of localised structures called motifs. To bridge the gap between localised structures and system-level architecture, we explored how motifs became pieced together and clustered in a broad range of real-world systems. Clustering was found to be pervasive, but striking differences were seen in the precise forms exhibited. We showed how these biases were linked to architectural features of the networks and in some cases remnants of their evolution by duplication-based processes. Furthermore, because duplication could not fully account for the biases seen, motif clustering may also have functional benefits that are positively selected for during evolution. These findings provide new opportunities to extract rules for the ways that motifs interact and evolve. This has implications for the analysis of existing systems and is of great use in the development of new complex systems. This thesis is organised into two parts. The first considers the theory and methods, and the second applies these to a range of complex systems.