Purpose: The purpose of this paper is to identify and discuss the most important initiatives and the strategic framework of the European Union (EU) supporting the 2030 Agenda for Sustainable Development. This paper also presents an overview of the progress towards the 4th Sustainable Development Goal (quality education) mainly in tertiary and adult education in the EU context. Design/methodology/approach: The adopted research method includes a literature survey, a study of law regulations and strategic documents of the EU and their critical analysis. The main axis of empirical investigation is a comparative analysis. Thematic scope of the analysis embraces indicators such as tertiary educational attainment, employment rate of recent graduates and adult participation in learning. Findings: The results of the comparative analysis confirm the diversity between Member States in achieving the goals of sustainable development. Overall positive trends in the development of quality education can be observed in the EU. However, the gender gaps in tertiary educational attainment and in the employment rate of recent graduates have been widening. Moreover, the EU is not on track to meet its 2020 benchmarks for adult participation in learning. Originality/value: The paper systematizes knowledge of initiatives of the EU for sustainable development and supplements it with a comparative analysis in the field of statistical data, which allows for a better understanding of the state and the prospects of implementing the idea of quality education at the EU level.