Characterization of the seismic hazard comprises undoubtedly the most critical component in probabilistic seismic risk assessment, and definitely the one associated with the largest amount of uncertainty. For applications involving dynamic analysis this hazard may be characterized through stochastic ground motion models. These models facilitate a versatile description of earthquake acceleration time-histories by modulating a stochastic sequence through functions that address spectral and temporal properties of the excitation. This is established by relating the parameters of these functions to earthquake and site characteristics though appropriate predictive relationships. There have been limited investigations, though, that examine the impact of the uncertainty in these predictive relationships on the seismic risk or that compare in detail the seismic risk provided through such stochastic ground motion models to other established approaches for describing seismic hazard (such as scaling of ground motions).  Motivated by this realization, the current research seeks to advance probabilistic seismic risk assessment by a) providing a better understanding of how stochastic ground motion models impact seismic risk, especially in terms of the uncertainty included in their predictive relationships, b) developing an efficient framework for a hazard compatible tuning of record-based models and c) investigating how these models can support probabilistic seismic risk assessment within the context of performance based earthquake engineering. A framework for comparison of existing ground motion models is first developed. This is established through a parametric investigation, examining seismic risk for different seismicity characteristics (such as moment magnitude and rupture distance of seismic events), but also through developing a global sensitivity analysis approach, aiming at identifying the importance of different risk factors towards the overall seismic risk. Extensive comparisons are made between two alternative ground motion models utilizing this framework and critical insight is provided for their relative benefits/drawbacks in characterizing seismic hazard. These models are also compared against Ground Motion Prediction Equations (GMPEs), corresponding to the established approach for characterizing seismic hazard, and potential discrepancies are identified. This motivates then the next component of the research, which is the selection/optimization of the predictive relationships of ground motion models so that compatibility to GMPEs is directly established. A versatile methodology is developed that allows the selection of seismicity and structural characteristics for this compatibility to be established, and then computationally efficiently performs the tuning of the chosen model. The foundation of the methodology is the development of a metamodel to approximate the median predictions of this chosen ground motion model and of the corresponding response quantities. The optimization can be then performed very quickly utilizing the developed surrogate model, providing the ability to tune the stochastic ground motion model to match specific GMPEs of interest. The impact of the use of stochastic ground motion models within the context of probabilistic seismic risk assessment is emphasized throughout the thesis. Discussion is also included at the end of the dissertation on how disaggregated information from hazard maps can be extended to a complete probabilistic description for regional seismological characteristics, which can then support a comprehensive risk assessment utilizing the proposed GMPE compatible ground motion modelling.