Abstract: Random matrix theory proved to be extremely useful in description and investigation of spectral properties of quantum chaotic systems. Parametric level dynamics is an attempt to understand various links between spectra of such systems and random matrices in the framework of statistical mechanics of a fictitious one-dimensional gas of interacting particles. I will review the geometric origin of the Hamiltonian formulation of level dynamics for various classes of quantum systems - autonomous and periodically driven, conservative and dissipative, pointing out achievements and difficulties of such an approach to justification of applicability of the random matrix to quantum chaotic phenomena.