Uniformization and selection for FO and MSO

Uniformization problem asks whether for a given formula phi(X,Y) there exists a formula psi(X,Y) that for every X selects exactly one Y satisfying phi(X,Y). Quite natural arguments show that MSO logic has uniformization property in finite and infinite words. During this talk I will survey classical results in the area. Additionally, I plan to present some new (and simple) observations; one of them states that FO does not have uniformization property even in finite words.