Methods for the analysis of highly excited vibrational eigenstates are presented. These include semiclassical and hierarchical analyses, along with a discussion of the nature of eigenstates along a correlation diagram. The purpose of the analyses is to extract information from what often appear to be complicated, ‘unassignable’ eigenstates. In particular, I address how to rationalize the nature of eigenstates via the semiclassical analysis and how to extract information concerning assignability and energy flow from the hierarchical analysis. The study of the eigenstates along a correlation diagram, together with the semiclassical analysis, is undertaken to address the issue of the classical-quantum correspondence when the classical mechanics is chaotic.