A collegiate university is a university in which functions are divided between a central administration and a number of constituent colleges. Historically, the first collegiate university was the University of Paris and its first college was the Collège des Dix-Huit. The two principal forms are residential college universities, where the central university is responsible for teaching and colleges may deliver some teaching but are primarily residential communities, and federal universities where the central university has an administrative role and the colleges may be residential but are primarily teaching institutions. The larger colleges or campuses of federal universities, such as University College London and University of California, Berkeley, may be effectively universities in their own right and often have their own student unions.

A red brick university was originally one of the nine civic universities founded in the major industrial cities of England in the 19th century.