After collapse of the Soviet Union new sovereign states that emerged on its territory faced pressing problems of economic survival and development, provision of social needs and prevention of a political chaos. Under these conditions an optimum outcome seemed to be to find a mutually beneficial model of interstate relationship between these countries which accepting new political realities would preserve (and then - develop) positive results of their long-term economic interaction in the framework of the USSR single national-economic complex. However, a rather long time was actually required before centrifugal tendencies in the post-Soviet space were replaced by centripetal ones. And only by the end of the first decade of the 21st century Russia, Kazakhstan and Byelorussia - the top post-Soviet states in terms of GNP - succeeded in coordinating their positions in favor of a mutual economic cooperation, being in fact of an integration character, and take a decision to create for this purpose first the Customs Union, then - the United Common Space and finally - the Eurasian Economic Union. The article presents analysis of basic achievements and shortcomings of these integration associations, explores the step-by-step progress of the Eurasian integration process as well as the role in its development of cooperation with foreign partners. Also, major challenges and threats facing Russian political and economic national interests in the post-Soviet space are explored and principal ways and means to be undertaken for their elimination or neutralization are outlined. Also, the article explores the current state and development prospects of the Eurasian Economic Union which functions in conditions of a deep global economic crisis caused by the coronavirus pandemic and problems at the world oil market. Besides these factors of a global character the EEU activities experience a serious negative impact of a number of regional problems and challenges - from a continuing regime of Western trade and economic sanctions and up to political maneuvers carried out by some EEU members (Armenia, Byelorussia) under slogans of multipolarity which resulted in a crisis of their domestic and foreign policies and also seriously undermined their participation in the EEU economic activities. General conclusion of the above analysis is made nevertheless in favor of positive prospects of the EEU development which has succeeded in preserving its viability under extreme conditions. This conclusion is also supported by all Union members officially stating their intention to continue their interaction and deepen mutual cooperation.