We discuss some of the models for eigenfunction localization in Hamiltonian systems. In particular, we review some of our work on classical parametric scaling of orbits and identification of localized states in a two-dimensional quartic oscillator system which is deep in the classically chaotic region. We show that visual methods are a necessary complement to quantitative methods based on information entropies. Our preliminary results indicate that the periodic orbit stability determines the degree of localization in a class of states, even when the stable regions are of negligible measure.

Computational methods for the calculation of a large number of eigenstates of coupled oscillator system are developed and discussed. These calculations have enabled us to identify and investigate properties of an infinite set of states sharply localized in configuration space in this system. Some of the results and their significance are discussed. Extensions to three-dimensional systems are also briefly considered.