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Perovskite materials possess a broad range of novel and useful properties. This has lead to perovskites being used in a broad range of applications, with considerable ongoing research being invested into them. While the bulk structure of these materials have been thoroughly investigated and documented, the polar surface and nanocluster structures of these compounds are relatively unknown. This is largely due to conventional structural determination techniques, such as X-ray and neutron scattering, proving ine ective on these non-bulk phases. In this thesis computational methods have been used to model the ABZ3 type perovskite materials KTaO3, KMgF3, and KZnF3. Global optimisation techniques have been employed to predict the structure of the compounds in non-bulk phases. The global optimisations were performed using interatomic potentials, with the lowest energy candidates being re ned through density functional theory. Reconstructions of the (001) polar KTaO3 surface were investigated. It was found that the lowest energy reconstructions involved the migration of the Ta ions from the surface, towards the bulk, where they were able to achieve a fuller coordination. The K ions moved in the opposite direction, migrating towards the surface. Defects in the form of neutral K and O vacancies were introduced to the surface. It was found that both types of vacancy resulted in an upward band bending towards the surface. This indicated an accumulation of holes at the surface for K vacancies, and an accumulation of electrons in the bulk for O vacancies. The structures of small nanoclusters, containing 5 - 100 atoms, were predicted for the compounds KMgF3 and KZnF3. The low energy structures revealed that it was energetically favourable for the B cations, Mg or Zn, to adopt positions close to the cluster centre, while the K cations resided at the edges of the clusters. The optical gap of the clusters was found to vary with the size of the cluster. This indicates the properties may be tuned by controlling cluster size.