World-Class Universities (WCUs) are nationally embedded comprehensive higher education institutions (HEIs) that are closely engaged in the global knowledge system. The article reviews the conditions of possibility and evolution of WCUs. Three interpretations are used to explain worldwide higher education: neoliberal theory, institutional theory, and critical political economy, which give greater recognition than the other theories to the role of the state and variations between states. World higher education is evolving under conditions of globalization, organizational modernization (the New Public Management), and in some countries, marketization. These larger conditions have become manifest in higher education in three widespread tendencies: massification, the WCU movement, and organizational expansion. The last includes the strengthening of the role of the large multi-disciplinary multi-purpose HEIs (“multiversities”), in the form of both research-intensive WCUs with significant global presence, and other HEIs. The role of binary sector and specialist HEIs has declined. Elite WCUs gain status and strategic advantage in both quantity and quality: through growth and the expansion of scope, and through selectivity and research concentration. The balance between quantity and quality is now resolved at larger average size and broader scope than before. The final section of the article reviews WCUs in China and considers whether they might constitute a distinctive university model.