Quantum dilatonic gravity in d=2, 4 and 5 dimensions

We review (mainly) quantum effects in the theories where the gravity sector is described by metric and dilaton. The one-loop effective action for dila tonic gravity in two and four dimensions is evaluated. Renormalization grou p equations are constructed. The conformal anomaly and induced effective ac tion for 2d and 4d dilaton coupled theories are found. It is applied to the study of quantum aspects of black hole thermodynamics, like calculation of Hawking radiation and quantum corrections to black hole parameters and inv estigation of quantum instability for such objects with multiple horizons. The use of the above effective action in the construction of nonsingular co smological models in Einstein or Brans-Dicke (super)gravity and investigati on of induced wormholes in supersymmetric Yang-Mills theory are given. 5d dilatonic gravity (bosonic sector of compactified IIB supergravity) is d iscussed in connection with bulk/boundary (or AdS/CFT) correspondence. Runn ing gauge coupling and quark-antiquark potential for boundary gauge theory at zero or nonzero temperature are calculated from d = 5 dilatonic anti-de Sitter-like background solution which represents anti-de Sitter black hole for periodic time.