Since 1990 there has been remarkable growth and diversification of worldwide capacity and output in science, and a distinctive global science system has emerged, primarily grounded in research universities, fostered by Internet-mediated communication and publication in English, cross-border authorship and researcher mobility. While global science overlaps with and is affected by national science systems, it is constituted by pan-national knowledge flows and collegial collaboration and has partial autonomy. Four different interpretive frameworks (narratives) have evolved to explain global science: science as an expanding cross-border network; science as an arms race between competing nations; science as a global market of competing 'World-Class Universities'; and science as a centre-periphery hierarchy in which emerging countries are permanently constrained by Euro-American dominance. The paper reviews each narrative in relation to the literature, especially in scientometrics, and empirical tendencies in global science, tracked in secondary data derived from bibliometric collections. While each narrative contains at least a grain of truth, each also conflicts with the others and each is radically insufficient. A better explanation of the drivers of global science combines (1) flat open networked relations with (2) the inequalities and closures shaped by global hegemony, arbitrarily modified by (3) national governments and specific resources.