This chapter provides some observations regarding the evolution of central banking. It is noted that the practice of monetary policy and the scope of central banks have changed over time. The chapter reflects on the path to East African Economic and Monetary Union (EA-EMU). First, how does East Africa stand in terms of economic and financial convergence? Second, what are the milestones of central banking that all central banks of the EA-EMU should master? Third, which monetary lessons could the euro area offer? Fourth, what worked, and has not, in the euro area, what is being fixed? It is noted that East African countries have differences in income per capita, exchange rate volatility, domestic prices, and fiscal discipline. To support sustainable convergence, they should align their monetary policy frameworks and have solid fiscal arrangement.