This article contributes to the ongoing debate about whether, how, and under what conditions latecomer countries can become producers of new technology and innovation, thereby catching up with technological leaders. Recent work on sectoral systems of innovation and in the evolutionary economics literature suggests that successful latecomers can move into new technological or industrial domains. They specialise in domains that present more frequent windows of opportunity, shorter technological cycles, flatter learning curves and easier access to relevant knowledge than others. This study investigates the role and significance of two hitherto neglected dimensions of technological regimes that might influence technological catch-up, namely, the degree of complexity and variety of an industry's knowledge base. The impact of technological variety and complexity on catch-up dynamics is tested in three industries - upstream oil/gas, wind power and solar energy - over the period from 1980 to 2016. First, we find that increased knowledge base complexity and related (as opposed to unrelated) variety play a substantial role by hindering the latecomers' attempts to catch up with technological leaders within each industry. Second, we confirm that other dimensions of technological regime are relevant. Specifically, we find that the length of the technological cycle is important, although a nuanced picture emerges regarding the direction of its impact on catch-up when results are compared across the three industries. These results offer new insights into the technologies and industries in which latecomer countries can specialise in order to develop their innovation capacity.