The application of a wide range of computational methods to several problems in zeolite chemistry is explored in this thesis. Symmetry-constrained lattice energy minimisations have been performed on a series of pure silica polymorphs using the shell model for silicates and quantitative agreement is found between the experimental and calculated structures. The computed lattice energies of the silicas are found to be between 8 and 20 kJmol^-1 less stable than quartz. The energies are found to be directly dependent on the densities of the structures and show good agreement with a recent calorimetric study. A new forcefield for aluminophosphates based on the shell model has been obtained by fitting to the structure and properties of berlinite and lattice energy minimisation calculations have been carried out on a series of aluminium phosphate polymorphs. The experimental structures are reproduced to a reasonable accuracy, especially in cases where high quality crystallographic data are available on calcined structures. In cases where experimental methods give conflicting results regarding the space group symmetry, calculated structures having lower symmetry than those observed in the crystallographic studies are suggested. An approximately linear dependence of lattice energy on density is again observed; the computed lattice energies are found to span a range of 11.7 kJmol^-1 higher than berlinite, which compares to an experimentally determined range of 9.7 kJmol^-1. Proton binding calculations have been performed on the structure of H-SAPO-37 to determine the most favourable binding proton sites. The calculations correctly reproduce the sites which have the highest fractional occupancies in a crystallographic study. Molecular dynamics simulation has been used to study the diffusion of xenon in ferrierite and zeolite-L. It was found that at 298K and a loading level of 1.33 atoms per unit cell, diffusion down the tenring channel in ferrierite is a more facile process than down the wider twelve-ring channel in zeolite-L (D=8.90xl0^-9 m²s^-1 for ferrierite versus 1.78xl0^-9 for zeolite-L). This effect can be rationalised by consideration of the effect of channel shape on the diffusion pathway. Under the same conditions, the interaction energy was calculated to be more favourable for ferrierite (ΔU=-25.7 kJmol^-1 versus -20.0 kJmol^-1). A new forcefield for the interaction of hydrocarbons and aromatics with siliceous zeolites was fitted to thermochemical and crystallographic data. The forcefield successfully reproduced the crystallographically determined positions of pyridine and propylamine in siliceous ferrierite and dodecasil-3C. In addition, quantum mechanical calculations were used to fit a forcefield for the interaction of benzene with cation-containing zeolites. Molecular dynamics calculations were used to study the transport of benzene in siliceous faujasite. The coupling of lattice vibrations to the benzene molecule was found to enhance the mobility (for example, at 298K, D=0.11xl0^-9m²s^-1 with a fixed lattice compared to D=0.31xl0^-9m²s^-1 with aflexible lattice). Two diffusion regimes were observed corresponding to intra- and inter-cage benzene mobility which correlate well with hypothetical hopping pathways. Analogous pathways for benzene in cation-containing zeolites have shown that cation sites act as traps for the benzene in Na-X and Na-Y, which reduce the mobility compared to the siliceous case. In Na-X, the pathways are further modified by the addition of extra cation sites that act to reduce the hopping activation energy and therefore enhance the diffusion. This behaviour is consistent with observed trends in experimentally determined diffusivities.