  In this thesis we study string theory with D-branes and possibly orientifolds
in curved or time-dependent spaces. Our study aims at understanding some
aspects of curved and time-dependent spaces, notably because of their
importance in cosmology.
  The first chapter introduces some bases of string theory.
  The second chapter studies non-oriented strings on compact groups SU(2) and
SO(3): after reviewing known results about D-branes in such spaces, we present
our results on the position of orientifolds and their interaction with open and
closed strings.
  The third chapter studies D-branes in certain backgrounds of Ramond-Ramond
type, using S-duality, which links them with backgrounds of Neveu-Schwarz type,
where calculations can be done.
  The last chapter considers strings on a D-brane embedded with a plane wave,
and introduces tools which allow to study interactions in such a background.
