  The stochastic Gross-Pitaevskii equation represents a versatile approach for
studying the dynamics of trapped degenerate ultracold Bose gases in the
presence of large phase and density fluctuations. Following a brief review of
the original formulation of Stoof, which highlights the benefits of this
approach and its relation to alternative theories, we present selected
applications for the dynamics of effectively one-dimensional systems, and
briefly discuss the generalization to two-dimensional systems, highlighting
certain potential pitfalls in their numerical implementations.
