We develop a two-country business-cycle model of the US and the rest of the world with dollar dominance in trade invoicing, in cross-border credit, and in safe assets. The interplay between these elements - dollar trinity - rationalizes salient features of the Global Financial Cycle in the data: When its tide subsides, the dollar appreciates, financial conditions tighten, the world business cycle slows down, and emerging-market central banks face a trade-off between mitigating the recession and dampening price pressures. We find the dollar is no sideshow in this, but central for the transmission of the Global Financial Cycle to the world economy.