The aim of the article is to review the existent theories of money and money definitions that result from them. What is still provided in the textbooks is, first of all, a classical definition of money which emphasasizes three basic functions that is serves which are: its transactional function, money as the measure of value and the thesaurus function of money. Secondly, money originates in the barter system. The classical definition was fully-justified until money could covered in precious metals, at least partly. Or this reason money cannot be currently expected to pay all three functions mentioned above. Hence the following hypothesis: First of all, the classical 3-functional money definition has been invalid for a longer while now. It is still existent in textbooks, It has become inert. Secondly, modern Anglo-Saxon literature makes a comeback to the perception of money as the product introduced by the State which is the main factor in the creation of the monetary system and regulation of monetary markets. It is included in the Modern Monetary Theory (MMT). Hence the second hypothesis. If we decide to support the idea of paper money dominance the definition of money has to include only two functions: money as a mean of transaction and as the measure of value. The thesaurus function is skipped as it is still desired, however not guaranteed (to a different degree and at different times). Simultaneously, a number of current historical analyses support the thesis that the traditional theory on the origin of money which is believed to come from the barter system cannot be supported any more. The concept of the barter is strongly criticized both in the Modern Monetary Theory and recently shaped theory stating that money is a contract (D. Graeber). The review of MMT points to discrepancies between a traditional classical 3-functional perception of money and the definition of money as a debt and it originating in the State. The last two approaches sometimes coincide and the form of paper money-Fiat Money can be explained only on their basis. The classical definition of money which is still present in textbooks would make sense if there was a comeback to money being covered in gold and if it was concluded that the fact it lacks cover is historically temporary. However it would be in total disagreement with the mainstream economic thoughts since Keynes times. At the same time serious accusations were formed against barter as the first stage of the origin of money.