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Relentless competition forces today’s universities to adjust quickly to changing trends in the market of education and science-intensive products and services. With the overabundance of approaches to competitiveness assessment, there is no universally applicable method that would evaluate a university comprehensively with due consideration of its specific nature. Over the last decade, the popularity of ranking systems has rocketed but the criticism thereof has also been on the increase. Thus, despite active research, the problem of the evaluation of university competitiveness requires development in both the theoretical and practical domains. Here, we analyse the tools for the international evaluation of university competitiveness based on current world rankings. The university performance indicators devised by the most reputable global rankings are reviewed and so are some alternative approaches. The paper focuses on the specific features and bottlenecks of the current world rankings as well as potential reasons for the underwhelming positions of the leading Russian universitie.