<p> Earthquakes and tsunamis represent two of the most devastating natural disasters faced by humankind. Earthquakes can occur in matters of seconds, with little to no warning. The governing variables of earthquakes, namely the stress profiles of vast regions of the earth's crust, cannot be measured in a comprehensive manner. Similarly, tsunami parameters are often accurately determined only minutes before waves make landfall. We are therefore left only with statistical analyses of past events to produce hazard forecasts for these disasters. Unfortunately, the events that cause the most damage also occur infrequently, and most regions have scientific records of earthquakes going back only a century, with modern instrumentation being widely distributed only in the past few decades. The 2011 <i>M=</i>9 Tohoku earthquake and tsunami, which killed close to sixteen thousand people, is the perfect case study of a country heavily invested in earthquake and tsunami risk reduction, yet being unprepared for a once-in-a-millennium event. </p><p> Physics-based simulations are some of the most promising tools for learning more about these systems. These tools can be used to study many thousands of years worth of synthetic seismicity. Additionally, scaling laws present in such complex geophysical systems can provide insights into dynamics otherwise hidden from view. This dissertation represents a collection of studies using these two tools. First, the Virtual Quake earthquake simulator is introduced, along with some of my contributions to its functionality and maintenance. A method based on Omori aftershock scaling is presented for verifying the spatial distribution of synthetic earthquakes produced by long-term simulators. The use of aftershock ground motion records to improve constraints on those same aftershock models is then explored. Finally, progress in constructing a tsunami early warning system based on the coupling of Virtual Quake and the Tsunami Squares wave simulator is presented. Taken together, these studies demonstrate the versatility and strength of complexity science and computational methods in the context of hazard analysis.</p><p>