The evolution of structure in biology is driven by accretion and diversification. Accretion brings together disparate parts to form bigger wholes. Diversification provides opportunities for growth and innovation. Here, we review patterns and processes that are responsible for a 'double tale' of accretion and diversification at various levels of complexity, from proteins and nucleic acids to high-rise building structures in cities. Parts are at first weakly linked and associate variously. As they diversify, they compete with each other and are selected for performance. The emerging interactions constrain their structure and associations. This causes parts to self-organise into modules with tight linkage. In a second phase, variants of the modules evolve and become new parts for a new generative cycle of higher-level organisation. Evolutionary genomics and network biology support the 'double tale' of structural module creation and validate an evolutionary principle of maximum abundance that drives the gain and loss of modules.