This thesis addresses two fundamental topics in Engineering Seismology; the application of Probabilistic Seismic Hazard Analysis (PSHA) methodology, and the estimation of measures of Strong Ground Motion. These two topics, while being related, are presented as separate sections. In the first section, state-of-the-art PSHA methodologies are applied to various sites in the Buller Region, South Island, New Zealand. These sites are deemed critical to the maintenance of economic stability in the region. A fault-source based seismicity model is developed for the region that is consistent with the governing tectonic loading, and seismic moment release of the region. In attempting to ensure this consistency the apparent anomaly between the rates of activity dictated by deformation throughout the Quaternary, and rates of activity dictated by observed seismicity is addressed. Individual fault source activity is determined following the application of a Bayesian Inference procedure in which observed earthquake events are attributed to causative faults in the study region. The activity of fault sources, in general, is assumed to be governed by bounded power law behaviour. An exception is made for the Alpine Fault which is modelled as a purely characteristic source. The calculation of rates of exceedance of various ground motion indices is made using a combination of Poissonian and time-dependent earthquake occurrence models. The various ground motion indices for which rates of exceedance are determined include peak ground acceleration, ordinates of 5% damped Spectral Acceleration, and Arias Intensity. The total hazard determined for each of these ground motion measures is decomposed using a four dimensional disaggregation procedure. From this disaggregation procedure, design earthquake scenarios are specified for the sites that are considered. The second part of the thesis is concerned with the estimation of ground motion measures that are more informative than the existing scalar measures that are available for use in New Zealand. Models are developed for the prediction of Fourier Amplitude Spectra (FAS) as well as Arias Intensity for use in the New Zealand environment. The FAS model can be used to generate ground motion time histories for use in structural and geotechnical analyses. Arias Intensity has been shown to be an important strong motion measure due to its positive correlation with damage in short period structures as well as its utility in predicting the onset of liquefaction and landslides. The models are based upon the analysis of a dataset of New Zealand Strong Motion records as well as supplementary near field records from major overseas events. While the two measures of ground motion intensity are strongly related, different methods have been adopted in order to develop the models. As part of the methodology used for the FAS model, Monte Carlo simulation coupled with a simple ray tracing procedure is employed to estimate source spectra from various New Zealand earthquakes and, consequently, a magnitude - corner-frequency relationship is obtained. In general, the parameters of the predictive equations are determined using the most state-of-the-art mixed effects regression procedures.