The process of random walk is described, in general, and how it can be applied in
the three-body problem in a systematic manner. Several applications are considered. The main one which is a focus of this paper is
on the evolution of horseshoe orbits and their transition to breakout motion in the restricted three-body problem.
is related to their use for an Earth-impactor in a theory on the formation of the Moon. We briefly discuss another
application on the instability of asteroid orbits.