Understanding of the dollar’s world role is dominated by the ideas of ‘dollar hegemony’ and ‘US hegemony’. In this paper, based on our extensive past work, we reveal how these ideas are ideologies, not theories. In their place, we reveal an understanding one that is theoretically sound and accords with the historical record, a geopolitical economy of the international monetary system of modern capitalism. We begin with a theoretical outline of how money operates under capitalism. We then consider how capitalism needs world money and, at the same time, makes its stable functioning difficult. We then go on to trace the fundamental instability of the modern international monetary systems based on national currencies of dominant countries, from the gold standard to the current volatile and predatory dollar-centred system, and their close connection to short-term and speculative.