In this article we illustrate what the contours of "Cliophysics" are. The term was coined by the "Cliometrics and Complexity" (CAC) team, composed of economists and physicists, and hosted by the Complex Systems Institute of ENS Lyon (IXXI). Cliophysics consists in the application of methodological tools from Complexity and Econophysics to the field of Economic history. More precisely, this new scientific challenge aims at combining Cliometrics, i.e. the application of economic modelling and econometrics to the field of Economic history, together with Complexity analysis and Econophysics. In this article, we highlight how using statistical signal processing, topological analysis and network analysis can enrich Cliometrics. To that end, we present three case studies taken from the research agenda developed within the CAC Team: 1) An original research in Cliophysics involving coïncidence analysis based on symbolic time series, aiming to revisit the classical standards of the link between public debt and economic growth in Economic history; 2) An approach in Cliophysics involving topological representations of asset markets networks, aiming to detect homogeneous eras of international monetary regimes; 3) An approach in Cliophysics involving the segmentation of multivariate time series derived from assets returns, aiming to allow for the identification of the structural breaks in the history of global capital markets. We provide evidence that Cliophysics 1) reveals new stylized facts in Economic history, 2) unveils key moments in the history of capital flows, different from the conventional view, and 3) fills a gap in historical analysis, by focusing on "structure matters in Economic history".