After the burst of the world financial crisis of 2007-2008 monetary policies, both in Europe and in the United States, by means of standard and nonstandard operations, have been pushed a long way beyond any limit previously attained, even in times of economic crises and depression. But these policies, while able to provide a support to the banking systems, appeared less successful as instruments to provide a general recovery of the real economies. The scope of the present paper is to investigate more properly the effects of the monetary policy of the European Central Bank (ECB) on the supply of money and on the level of credit to the real economy, namely to nonfinancial firms and corporations and to households in the euro area in order to clarify the real goals of this policy. A set of interesting relationships can be found between the monetary base and the supply of money and between the supply of money and credit to the real economy. The role of the banking systems in the transmission mechanism of monetary policy is stressed, while the shortcomings of this policy with regard to the proper functioning of the money markets - owing to an enduring situation of negative real interest rates - and to the building of a noninflationary exit strategy from the crisis are highlighted.