Increased urbanization, mass migration towards cities, and climate change have drastically increased the vulnerability of our communities to natural hazards, creating increased urgency for comprehensive hazard/risk assessment strategies that can better inform risk mitigation strategies and real-time emergency responses. To facilitate such a comprehensive assessment, these strategies need to rely on the use of high-fidelity numerical models, creating a significant computational burden that is still considered as insurmountable for many applications. This work investigates the implementation of surrogate modeling techniques to address this challenge. Kriging is adopted as the preferred surrogate model, and two different hazard implementations are examined: (i) the estimation of storm surge, and (ii) the approximation of engineering demand parameters (EDPs) for earthquake applications that use stochastic ground motion models for the description of the seismic hazard. Emphasis is placed on the former, that also represents an application with renewed importance due to the widely acknowledged increased vulnerability of coastal communities stemming from future sea level rise and storm intensification projections.Using synthetic storm databases developed for coastal studies as the foundation of the surrogate model development, various unexplored topics are investigated in detail for the formulation of surrogate models to predict the peak storm surge. These include topics related to the incorporation of sea level rise explicitly as an input in the surrogate model formulation with additional guidance for the development of such synthetic storm databases, and the efficient risk assessment for extended regions of interest with hundreds of thousands of points for which the hazard curves need to be estimated. Other developments investigate, the surrogate model implementation for small size databases, examining in more detail any occurring overfitting challenges, the explicit use of a classifier to accommodate higher accuracy for nodes that have remained dry in some storms, and finally, the detailed exploration of different surrogate modeling approaches that can accommodate time-series surge predictions. For seismic applications, the research in this dissertation advances the estimation of the EDP distribution. Emphasis is placed on efficiently addressing the aleatoric uncertainty related to the hazard description within a surrogate modeling framework. This is accommodated by leveraging the nugget parameter in the kriging formulation and by introducing a novel stochastic kriging implementation that allows a heteroscedastic description of the nugget variance. Implementation greatly reduces the number of structural simulations for the calibration of the metamodel that approximates the EDP distribution, promoting significant computational savings in seismic risk assessment application.