This paper is devoted to changes in the structure of the higher education system in Russia, analysing both historical context and current institutional diversity. The review starts from the Soviet quasi-corporate system when the state combined demand-side and supply-side roles in higher education. The post-Soviet transformation brings new forces that shaped institutional diversity. Following that, the historical typology of institutions is investigated with regard to the major forces influencing these universities' development. Taking into account both the historical legacy and the crucial post-Soviet period (1990s-2000s), a typology of new types of higher education institutions is set forth. It represents an extreme case of state-authorized higher education facing market forces. The state abandons its monopoly on demand in higher education and cannot fully control the supply side. And the system itself is under pressure from the influence of different sides.