This paper presents a critical assessment of the widely discussed concept of Islamic Economics. The two different interpretations of Islamic economics as the study of the functioning of an interest-free economy and the validity of moral values in the economy are discussed. It is shown that none of these interpretations can help to create an acceptable foundation for an Islamic economics. Far away from laying the foundation for such an economics the question is raised how an Islamic economy would function, based on the Islamic principle of controlling the Nafs. Microeconomics and macroeconomics of such an economy are analysed and its special features are compared to an economy functioning on the basis of laws devised by the conventional economic analysis.