Thesis: Earthquake rates are a key component of probabilistic seismic hazard and risk assessment. A novel methodology to model earthquake rates in complex ruptures in a fault system (SHERIFS) is developed. The flexibility of the methodology allows sharing it and applying it to various fault systems as well as using it as a tool to discuss the hypotheses concerning the seismicity on faults. The earthquake rates in the Western Corinth Rift in Greece and the Marmara Region in Turkey are modeled while exploring the associated epistemic uncertainty such as on the maximum rupture scenario, the magnitude frequency distribution or the locking condition of the faults. In Marmara, the hypotheses are weighted in a logic tree by comparing them to the rate calculated from the data (earthquake catalog and paleoseismicity) and the results of a “physics-based” model applying the rate and state equations. For each hypothesis in the logic tree, the seismic risk in Istanbul, represented by the probability of collapse of a building, is calculated for two buildings of the same type but one constructed following the 1975 building code and on following the 1998 building code. The seismic risk is six times larger for the older building. Within the explored uncertainties, the one concerning the magnitude frequency distribution is the largest source of uncertainty on the risk of collapse. By using the data and the physics-based model to weight the logic tree, the uncertainty on the risk is reduced by a factor of 1.6. Through a novel risk deaggregation methodology, we identify two seismogenic sources controlling the risk in Istanbul: the large earthquakes (magnitude larger than 7) on the neighboring North Anatolian Fault and the moderate magnitude earthquakes (magnitude between 4.5 and 6) occurring in the background zone, on unknown faults, and at a distance shorter than 10 km from the building.