Achievement of stable economic growth and ensuring innovative development, the needs of the creative economy for specialists with digital skills can be considered as one of the main challenges for the sphere of tertiary education. Therefore, the education system should provide a high level of service quality in order to meet the needs of labor markets. Globalization and international cooperation between the EU and Asia exacerbate these problematic issues. The purpose of the research lies in systematizing the basic challenges of the external environment and their impact on the transformation and development trends of tertiary education on the example of the EU states. Methodology. The research is based on quantitative methodology and statistical analysis. The development indicators of higher education of the EU countries for 2013-2018 from the database of Eurostat and the World Bank have been used for the analysis. The results prove the complexity of the links between social-economic, environmental and political issues, which determine the dynamics of tertiary education and transformational changes in tertiary education. The following key challenges have been highlighted in the academic paper, namely: 1) development of creative economy, innovation economy and knowledge economy; 2) external shocks, such as a pandemic; 3) technological progress and integration of technologies into education; 4) increasing the level of migration flows and strengthening the problem of educational inequality; 5) spreading the practice of commercialization and privatization of tertiary educational institutions (TEIs); 6) globalization and internationalization of tertiary education due to international cooperation between different countries and regions.Keywords: external shocks in education, internationalization of tertiary education, trends in the EU tertiary education, neoliberalism in tertiary education.