In this paper we briefly review the macroeconomic theory of inflation, relating it to the recent developments in the advanced economies. Then, we analyse the drivers of the rise in inflation observed in 2021 in the United States and in Europe, and we illustrate the factors that may affect the inflationary scenario of the advanced economies in the longer term. Finally, we discuss what challenges the Federal Reserve and the European Central Bank have to meet in the face of current inflationary pressures. This paper was provided by the Policy Department for Economic, Scientific and Quality of Life Policies at the request of the committee on Economic and Monetary Affairs (ECON) ahead of the Monetary Dialogue with the ECB President on 27 September 2021.