Abstract: The semiclassical approach to quantum gravity is the most developed sector on the intersection of our quantum and gravitational knowledge. One can say that the main achievements in this area are strongly related to conformal (trace) anomaly. In the talk we are going to consider the origin of anomaly, its ambiguities and its use for deriving the effective action of gravity. The possibility to go beyond the limits of the one-loop approximation is reviewed. Furthermore, we will explore the most important applications, such as Starobinsky model of inflation and classification of the quantum states of quantum fields in the vicinity of a black hole.