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