The present article analyses the main shifts in the global system and in the relations between Russia and the West associated with the start of a new geopolitical and geoeconomic revolution (revolution of the global market). It is shown that the growing tension in the relations between Western countries and Russia are long-term and non-accidental. It is caused primarily by the profound social divisions and domestic political conflict in the USA and in the EU countries; and at a global scale – by economic crises and establishment of the new world order, the shift of the center of economic development from the West to the East. Among the mainstream trends that form the outlines of the new world order are strengthening of China and other Asian countries, the delocalization of the global center of political and economic power, the increasing strife in international relations (in particular, in the relations between the collective West and Russia), and the declining economic and political role of the united Europe. With the account of the previously described interaction between the evolutionary cycles of the world political and economic system and the 36-years cycles of the Russian political history there are revealed the major thresholds in the development of the Western countries and Russia during the 2020s, namely: the period from 2021 to 2022, the period from 2024 to 2025 and from 2029 to 2030. Basing on the correlation of the phases of revolution of the global market as well as on the analysis of current political processes, we make a conclusion that the period from 2021 to 2025 will be especially challenging and full of conflicts; moreover, the domestic political splits in the USA and European countries will provoke regional military and political conflicts between Western states and Russia. We anticipate the reshaping of political systems in Russia and the USA after 2024–2025.