The shocks of the twentieth century and the crisis phenomena of the early twenty-first require from political economists new approaches to the interpretation of the changes taking place in the current economy. The dynamism and contradictory nature of the market economy is based on competition, which is the source of formal and real subordination of labour to capital. The competition that was available in the 19th and 20th centuries has disappeared from the historical arena. It has been replaced by conflict, raiding and sanctions. During the comparison of economic theories, there is a discussion of methodology, which is the basis for the development of procedures and forecasts. Despite the fact that the history of economic thought and economic history cannot give contemporaries a clear model of the development of society in the 21st century, some clues are still present. The article traces changes in the content and forms of manifestation of the concepts of the highest rank of complexity (global competition, the legacy of K. Marx and Marxism, late capitalism, the history of political economy as a space of reflexion in the 21st century). Modifications of meaning in the evolution of concepts are taken into account: historical time, epoch, century trends, generational approach. The sources of information possessing novelty from the point of view of introducing new concepts relevant for the modern stage of society development into the scientific turnover have been introduced. Hypotheses (theses - assumptions) regarding the development trajectory of Russia and the world in the current decade are put forward for discussion. Each section of the article is autonomous and has a non-trivial value.