Studied in the article are international political processes taking place since the end of World War II. It is shown that the modern world is in a state of transition to a multipolar world order – a process based on the foundation components left from the era of bipolarity. Analyzed is the phenomenon of “superpower leadership” and its transformation at the turn of 1980?1990s, descent, sometimes painful, of superpowers to the ranks of “ordinary” great powers, search for grounds for building relations between them on an equal footing. Marked are the symptoms of the shift of the global centre of power and influence in the 21st century from the USA to China. Evaluated is development of Russian-American relations, as well as claims of the European Union on the role of another large and influential centre in the future multipolar world.