The European Central Bank (ECB) assigns greater weight to the role of money in its monetary policy strategy than most, if not all, other major central banks. Nevertheless, reflecting the view that the demand for money became unstable in the early 2000s, some commentators have reported that the ECB has “downgraded” the role of money demand functions in its strategy. This paper explains the ECB’s monetary policy strategy and shows the considerable influence of Milton Friedman’s contributions on the formulation of that strategy. The paper also provides new evidence on the stability of euro area money demand. Following a conjecture made by Friedman (1956), the authors assign a role to uncertainty in the money demand function. They find that although uncertainty is nonstationary and subject to wide swings, it is nonetheless mean reverting and has substantial effects on the demand for money.