  Concise review of the basic properties of unitary matrix integrals. They are
studied with the help of the three matrix models: the ordinary unitary model,
Brezin-Gross-Witten model and the Harish-Charndra-Itzykson-Zuber model.
Especial attention is paid to the tricky sides of the story, from De
Wit-t'Hooft anomaly in unitary integrals to the problem of correlators with
Itzykson-Zuber measure. Of technical tools emphasized is the method of
character expansions. The subject of unitary integrals remains highly
under-investigated and a lot of new results are expected in this field when it
attracts sufficient attention.
