This paper studies the transformation of the International Monetary System (IMS) in the run up to and after the 2007-9 Financial Crisis. Adopting a Money View perspective, it argues that the IMS, in contrast to widespread skepticism, does have a system-like quality. This paper understands the IMS as a US-centered hierarchical payments system within which short-term debt instruments are issued as credit money by various public and private financial institutions, in particular central, commercial and shadow banks. With the Fed located at the apex of the IMS, credit money forms denominated in US dollars are located highest up in the hierarchy and trade at par with each other, whilst they typically have fluctuating exchange rates to credit money forms denominated in the units of account of other monetary jurisdictions. From this, the paper argues that the key component of today's IMS is the 'realm' of offshore US dollar creation, which is situated in between US dollar-denominated credit money issued in the US ('onshore dollars') and non-US dollar-denominated credit money issued outside the US. In this 'offshore dollar realm', non-US financial institutions are able to create international liquidity via US dollar-denominated private credit money outside the US. The paper systematically carves out the post-2008 setup of the offshore dollar realm with a focus on Eurodollar deposits, offshore money market fund shares, foreign exchange swaps and central bank swaps. With the institutional innovations materializing during the 2007-9 Financial Crisis, the IMS is now a publicprivate hybrid that fully mirrors the onshore US monetary system in the offshore dollar realm.