Title: "Local Conformal Symmetry and its Violation at Quantum Level"

The purpose of this talk is to present a short review of the local conformal symmetry in curved $4d$ space-time. Furthermore we discuss the conformal anomaly, anomaly-induced effective actions and existing ambiguities. Despite the conformal symmetry is always broken at quantum level, it may be a basis of useful and interesting approximations for investigating quantum corrections. These quantum corrections represent an appropriate basis for a number of applications in cosmology and black hole physics.