  We explore the recently introduced statefinder parameters. After reviewing
their basic properties, we calculate the statefinder parameters for a variety
of cosmological models, and investigate their usefulness as a means of
theoretical classification of dark energy models. We then go on to consider
their use in obtaining constraints on dark energy from present and future
supernovae type Ia data sets. Provided that the statefinder parameters can be
extracted unambiguously from the data, they give a good visual impression of
where the correct model should lie. However, it is non-trivial to extract the
statefinders from the data in a model-independent way, and one of our results
indicates that an expansion of the dark energy density to second order in the
redshift is inadequate. Hence, while a useful theoretical and visual tool,
applying the statefinders to observations is not straightforward.
