CONFORMAL ANOMALIES - RECENT PROGRESS

We present a brief review of some recent results on conformal anomalie s in four and more dimensions. The discussion is intended for relativi sts, so some background on the quantum origin of anomalies and of thei r simple properties in D=2 is also provided. Topics treated include a critical review of the effective gravitational action uniqueness probl em and the derivation of beta functions, independent of ultraviolet be havior, from the type B anomaly.