<p> Earthquakes are among the most devastating natural events faced by society. In 2011, just two events, the magnitude 6.3 earthquake in Christcurch New Zealand on February 22, and the magnitude 9.0 T&omacr;hoku earthquake off the coast of Japan on March 11, caused a combined total of $226 billion in economic losses. Over the last decade, 791,721 deaths were caused by earthquakes. Yet, despite their impact, our ability to accurately predict when earthquakes will occur is limited. This is due, in large part, to the fact that the fault systems that produce earthquakes are non-linear. The result being that very small differences in the systems now result in very big differences in the future, making forecasting difficult. In spite of this, there are patterns that exist in earthquake data. These patterns are often in the form of frequency-magnitude scaling relations that relate the number of smaller events observed to the number of larger events observed. In many cases these scaling relations show consistent behavior over a wide range of scales. This consistency forms the basis of most forecasting techniques. However, the utility of these scaling relations is limited by the size of the earthquake catalogs which, especially in the case of large events, are fairly small and limited to a few 100 years of events.</p><p> In this dissertation I discuss three areas of earthquake science. The first is an overview of scaling behavior in a variety of complex systems, both models and natural systems. The focus of this area is to understand how this scaling behavior breaks down. The second is a description of the development and testing of an earthquake simulator called Virtual California designed to extend the observed catalog of earthquakes in California. This simulator uses novel techniques borrowed from statistical physics to enable the modeling of large fault systems over long periods of time. The third is an evaluation of existing earthquake forecasts, which focuses on the Regional Earthquake Likelihood Models (RELM) test: the first competitive test of earthquake forecasts in California.</p>