The development of information technologies and tools of customs compliance control occurs at the interdisciplinary field of system audit, logistics and information management. One of the prospective directions of Russian customs control modernization is the development and implementation of information technologies of customs compliance that provides simplification and expedition of customs procedures due to the risk-management, the selectivity and the building of a single information space. The purpose of the article is to define the prospects and problems of applying information technologies of compliance control to Russian customs and international trade activities. The authors analyze such compliance information technologies as process mining, smart audit, IT-sourcing. Research results show that organizational, legal and institutional development of customs compliance will contribute to the dynamic and clear relations “Customs-Business” in Russia, the risk management system, effective categorization of traders.