The theory of periodic orbits for conservative Hamiltonian systems and the way that it is applied to analyse vibrational spectra of highly excited polyatomic molecules is reviewed. Applications for triatomic, tetratomic molecules and van der Waals clusters are presented. It is shown that the periodic orbit method can trace localized eigenfunctions above potential barriers which are associated with saddle-node bifurcations. Such states connect separate minima on the potential energy surface, and thus, are important for studying isomerization processes.