  The classical Bondi-Penrose approach to the gravitational radiation theory in
asymptotically flat spacetimes is recalled and recent advances in the proofs of
the existence of such spacetimes are briefly reviewed. We then mention the
unique role of the boost-rotation symmetric spacetimes, representing uniformly
accelerated objects, as the only explicit radiative solutions known which are
asymptotically flat; they are used as test beds in numerical relativity and
approximation methods.
  The main part of the review is devoted to the examples of radiative fields in
the vacuum spacetimes with positive cosmological constant. Type N solutions are
analyzed by using the equation of geodesic deviation. Both these and
Robinson-Trautman solutions of type II are shown to approach de Sitter universe
asymptotically. Recent work on the the radiative fields due to uniformly
accelerated charges in de Sitter spacetime ("cosmological Born's solutions") is
reviewed and the properties of these fields are discussed with a perspective to
characterize general features of radiative fields near a de Sitter-like
infinity.
