Criminal methodology examines specificity of individual groups and individual criminal acts in terms of their causes and conditions, manner and means of perpetration, manifestation, tactics and techniques of perpetrators. On this basis, one finds and applies specific methods and means for their individual detection, clarification and proofing, and detection of perpetrators. Criminal methodology uses criminal-tactical and criminal-technical methods and means, adapting them to individual crimes, while also developing its own methods. This paper clarifies the notion and subject of criminal methodology as a scientific discipline of criminalistics as the science. The concept of economic criminality has been defined, and particularly the problem of criminal acts of economic crime as one of the most dangerous and most harmful forms of this negative social phenomenon. Furthermore, the characteristics of economic criminality, as well as the classification of its manifestation, have been considered. The classic manifestation forms and criminal activities by sectors of economic activities, which occur in all periods of development of our society, have been analyzed. They are constant with slight modifications in the way of perpetration and concealment, and contemporary manifestation forms of economic crime that are the result of new tendencies in social, political and economic relations. In addition, the detection of criminal acts of economic crime and the provision of evidence have been considered through the operational activities of the police that are conducted in pre-trial procedure through two basic stages: criminal control and criminal investigation. Moreover, the methodology for discovering and proving typical offenses of economic crime, that is criminal acts with basic characteristics and manner of perpetration, has been presented and analyzed, and a brief review of the legislative framework, activities and results that the police have achieved in suppressing and preventing these phenomena has been given.