"Central banking" is what a central bank does, but the definition of "central bank" is less straightforward than it may appear at first sight. Following Ugolini (2017), this chapter defines central banking as the provision of public policies aimed at fostering monetary and financial stability, and surveys the historical evolution of such policies in the West from the Middle Ages to today. It shows that institutional equilibria mattered a lot in shaping the way stabilization policies were implemented: central banking evolved in markedly distinct ways in city states (like Venice, Amsterdam, Hamburg, Barcelona, or Genoa), centralized territorial polities (like Naples, Sweden, England, Austria, or France), or decentralized territorial polities (like the United States or the European Union). As a result, the historical evolution of central banking does not appear to have been driven by the "survival of the fittest", but rather by the constant adaptation of policymaking to changing political economy equilibria.