Current world order is in crisis and in process of reshaping. However, mainstream of Western analysts and political-academic community of Russia interpret differently and often alternatively the definition and parameters of the world order, as well as manifestations of its crisis. The author investigates the conceptual framework of describing evolution of international system in terms of changing periods of relative stabilization (order with widely recognized rules) and periods of disorder (transits). The article compares modern Russian and international concepts of world order, periodic sequencing of stable and destabilized stages of international system, analyzes varying definitions and historical periodization of world order. The areas and manifestations of the crisis of the previous model of world order are revealed, as well as directions of undermining strategic stability and erosion of the system of arms control and disarmament. The author poses the question whether the level of general “systematization” of international relations is high enough to perceive the international relations as unified “system with rules”, or whether the world remains a set of weakly related regional agglomerations. The article probes alternative hypotheses, whether post-bipolar period since the end of the Cold war is the new format of world order based upon principles of international behavior coordinated between Russia and the West. The author also considers whether the sharpening of international tensions after 2014 manifested the crisis of that format of world order, or international processes of last three decades after the end of the Cold war represent just fluctuations within trajectory of evolution of world order established after the end of the WW2 since mid-20th century until modern times. The author sketches directions of reformation of the world order from the angle of Russian national interests and in view of tendencies of current and prospective evolution of the international system.