  The concept of random dynamical system is a comparatively recent development
combining ideas and methods from the well developed areas of probability theory
and dynamical systems.
  Due to our inaccurate knowledge of the particular physical system or due to
computational or theoretical limitations (lack of sufficient computational
power, inefficient algorithms or insufficiently developed mathematical or
physical theory, for example), the mathematical models never correspond exactly
to the phenomenon they are meant to model. Moreover when considering practical
systems we cannot avoid either external noise or measurement or inaccuracy
errors, so every realistic mathematical model should allow for small errors
along orbits not to disturb too much the long term behavior. To be able to cope
with unavoidable uncertainty about the ``correct'' parameter values, observed
initial states and even the specific mathematical formulation involved, we let
randomness be embedded within the model to begin with.
  We present the most basic classes of models in what follows, then define the
general concept and present some developments and examples of applications.
