Which countries benefit most from emerging technological opportunities? An enquiry into the changing geography of knowledge base complexity in the upstream petroleum industry This article aims to unravel the relationship between dynamics of knowledge base complexity and the international geography of innovation with particular emphasis on understanding catch-up processes. Putting the distinction between breadth and systemic complexity at the centre of analysis of the sectorial knowledge base, this research contributes to our understanding of the changing geography of knowledge base complexity. We argue that systemic complexity implies higher geographical proximity, because coordination and integration of different pieces of knowledge is challenging over long distances when there are intensive interactions. However, if the complexity is more of the breadth type and systemic interactions are limited, the possibility of geographical dispersion is higher. This distinction clarifies some of the ambiguities and inconsistencies in the literature with regard to the geographical implications of complexity. In fact, different dimensions of complexity have different geographical impacts. As formulated in our research hypothesis, we expect a higher number of new entries and more opportunities for latecomer catch-up, and therefore more rapid geographical dispersion, when systemic complexity is low and breadth complexity is dominant. In contrast, increasing systemic complexity implies higher barriers to entry, fewer catch-up opportunities, and slower geographical dispersion (or even higher geographical concentration). Relying on patent data, we found empirical evidence to support the hypothesis in the upstream petroleum industry. In addition, the results suggest that in dealing with systemic complexity, the cognitive and organizational proximity available in internal networks of big multinational companies may be more important than geographical proximity. The empirical results also offer some theoretical insights about the dynamics of geographical patterns of innovation. In the last period studied, we observed a high geographical dispersion of innovative activities in conjunction with a highly concentrated ownership structure. This is consistent with the nature of systemic complexity which dominated in that period, creating scale, scope and agglomeration economies. This conditions favour big multinational companies of advanced countries. Although their innovative activities are geographically distributed, in terms of ownership, they control a lion share of innovative activities in the sector. These findings offer valuable insights regarding the development of a dynamic theory of the geography of knowledge base complexity, as an interesting area for further research.