  In this review, an overview of the recent history of stochastic differential
equations (SDEs) in application to particle transport problems in space physics
and astrophysics is given. The aim is to present a helpful working guide to the
literature and at the same time introduce key principles of the SDE approach
via "toy models". Using these examples, we hope to provide an easy way for
newcomers to the field to use such methods in their own research. Aspects
covered are the solar modulation of cosmic rays, diffusive shock acceleration,
galactic cosmic ray propagation and solar energetic particle transport. We
believe that the SDE method, due to its simplicity and computational efficiency
on modern computer architectures, will be of significant relevance in energetic
particle studies in the years to come.
