  Understanding the geometry and topology of configuration or conformational
spaces of molecules has relevant applications in chemistry and biology such as
the proteins folding problem, drug design and the structure activity
relationship problem. Despite their relevance, configuration spaces of
molecules are only partially understood. In this paper we discuss both
theoretical and computational approaches to the configuration spaces of
molecules and their associated energy landscapes. Our mathematical approach
shows that when symmetries of the molecules are taken into account,
configuration spaces of molecules give rise to certain principal bundles and
orbifolds. We also make use of a variety of geometric and topological tools for
data analysis to study the topology and geometry of these spaces.
