My work focused on the development of improved methodologies for the evaluation of seismic hazard and its related uncertainties, based on the study of active faults systems and dynamic modelling of the seismic cycle. I worked in particular on the probabilistic estimate of a fault‘s maximum magnitude earthquake and of its return period. Those parameters are indeed crucial to estimate seismic hazard. Seismicity can be viewed as a stochastic process which is constrained by the principle of moment conservation: seismic ruptures must in principle rupture fault portions which had accumulated a deficit of slip, in view of their long term slip rate, during the interseismic period. In Chapter 1, I explain how we implemented those constraints in the evaluation of the probability distribution describing the magnitude and return period of the largest earthquake, propagating the geodetic uncertainties up to the hazard calculation. We applied this methodology to the Parkfield Segment of the San Andreas Fault, where the seismic cycle is particularly well documented. Our study implies potential maximum magnitude between 6.5 and 7.5, with a return period of 140 to 300 years. In Chapter 2, we applied the same methodology to the Cascadia subduction zone, known to have produced a M~9 earthquake in 1700 but where the seismic hazard remains poorly constrained. As part of this study we determined a model of interseismic coupling and of fault slip due to Slow Slip Events using an Independent Component Analysis-based inversion method. Finally, in Chapter 3, I use dynamic modelling to tackle the problem of partial ruptures. Large earthquakes tend to be confined to fault areas locked in the interseismic period but they often rupture them only partially. For example, during the 2015 M7.8 Gorkha earthquake, Nepal, a slip pulse propagating along-strike unzipped the bottom edge of the locked portion of the Main Himalayan Thrust. The lower edge of the rupture produced dominant high-frequency (>1 Hz) radiation of seismic waves. We showed that similar partial ruptures occur spontaneously in a simple dynamic model of earthquake sequences on a planar fault without mechanical, frictional and geometrical heterogeneities.