The article presents a historiographical review of assessments of higher education and science development in Asia, which has now become the key economic region of the world. It is a common knowledge that education, science and innovations represent a driving force of economic development and indispensable for building a knowledge-based economy. The analysis presented in this article adds to a better understanding of knowledge-based economy development in Greater Eastern Asia. The article presents the research literature and science metrics analysis on science and education development in Asia dividing it into four clusters. International organizations (e.g., the UN and OECD) and transnational ranking agencies (like QS) judging by the quantitative indicators point out that Greater Eastern Asia (Northeast Asia, Southeast Asia and India) has become one of the world leaders in terms of higher education development and innovations. In high technologies, the region is second only to the USA and is constantly bridging this gap. Greater Middle East (the Middle East and Central Asia) looks differently in this respect. Arab countries' opportunities to build knowledge-based economy are very limited as well as those of Central Asia. In terms of quality of science and education Greater Eastern Asia (with the exception of the most advanced countries of the region) is still lagging behind the West and in terms of fundamental science this gap looks very serious. However, there are efforts in place to make the rise of science and education in Asia more quality-oriented, for instance focusing more on strengthening engineering and hard science in the Asian universities.