The evolution of the IMS and IFS in the past several hundred years can be viewed through the lens of the Copernican heliocentric system developed over 500 years ago. We trace out the evolution across regimes of the IMS and IFS in terms of network representations of the Copernican system. We provide a simple, fully testable theoretical model whose assumptions are based on these representations. The IMS and IFS are described by a two-layer graph whose three key features (hub, core, distances) are affected by nonlinear joint regime changes linked to a technological, institutional, geopolitical and regulatory environment variable. We conclude with a discussion of some perspectives of the future of the international monetary and financial systems. Our analysis is based on economic history, theory and some resonant concepts from astrophysics.