The reform of national education systems is driven by rapid technological and economic change, unequal access to quality education, the digital economy, the growing mobility of students and teachers, the alignment of qualifications with international standards, the changing role of the teacher (tutor, facilitator, mentor) and the development of lifelong learning. Under these conditions, teacher education has to adopt international standards and good practice and remain flexible, and its leading paradigm is the competency-based approach. The aim of this study is to analyse current trends in the development of pedagogical education and to substantiate competency-based education in the natural sciences, using the innovative educational programmes introduced at Abai Kazakh National Pedagogical University as an example. The study is conceptual and analytical: publications identified in Scopus, Web of Science and Google Scholar, policy documents and programme documentation were examined by content and comparative analysis. The results systematize the main research areas, specify the structural components of competency-based education (target, content, process, assessment, resource and reflective components) and compare international and domestic research on scientific and functional literacy, research competence, digital competence and problem solving in the natural sciences. The implementation of the approach is illustrated by the educational programme 6B01515-Geography, in which new courses link subject knowledge with research-based, practice-oriented, STEM and CLIL teaching and with the Sustainable Development Goals. The study concludes that the successful implementation of competency-based programmes depends on their methodological support and on the continuous professional development of university teachers, and it formulates practical recommendations for programme developers and teaching staff.