We first review earlier work in which we computed the first-principles structural, vibrational, and lattice dielectric properties of the cubic, tetragonal, and monoclinic phases of ZrO2, and HfO2. We then discuss two approaches to the construction of realistic models of amorphous ZrO2: a "melt-and-quench" ab-initio molecular dynamics approach, and an "activation-relaxation technique". The structural, vibrational, and dielectric properties of the resulting models are then analyzed in detail. The overall average dielectric constant is computed and found to be comparable to that of the monoclinic phase. These techniques show promise for future modeling of high-K dielectric ultrathin films and interfaces. (c) 2005 Elsevier B.V. All rights reserved.