  Before we apply nonlinear techniques, for example those inspired by chaos
theory, to dynamical phenomena occurring in nature, it is necessary to first
ask if the use of such advanced techniques is justified "by the data". While
many processes in nature seem very unlikely a priori to be linear, the possible
nonlinear nature might not be evident in specific aspects of their dynamics.
The method of surrogate data has become a very popular tool to address such a
question. However, while it was meant to provide a statistically rigorous,
foolproof framework, some limitations and caveats have shown up in its
practical use. In this paper, recent efforts to understand the caveats, avoid
the pitfalls, and to overcome some of the limitations, are reviewed and
augmented by new material. In particular, we will discuss specific as well as
more general approaches to constrained randomisation, providing a full range of
examples. New algorithms will be introduced for unevenly sampled and
multivariate data and for surrogate spike trains. The main limitation, which
lies in the interpretability of the test results, will be illustrated through
instructive case studies. We will also discuss some implementational aspects of
the realisation of these methods in the TISEAN
(http://www.mpipks-dresden.mpg.de/~tisean) software package.
