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The catastrophic occurrence of the 2004 M9.2 Sumatra and 2011 M9.0 Tohoku earthquakes illustrated the disastrous impact of megathrust earthquakes on society. They also emphasized our limited understanding of where and when these ”big ones” may strike. The necessary improvement of long-term seismic hazard assessment requires a better physical understanding of the seismic cycle at these seismically active subduction zones. Models have the potential to overcome the restricted, direct observations in space and time. Currently, however, no model exists to explore the relation between long-term subduction dynamics and relating deformation and short-term seismogenesis. The development, validation and initial application of such a physically consistent seismo-thermo-mechanical numerical model is the main objective of this thesis. First, I present a novel analog modeling tool that simulates cycling of megathrust earthquakes in a visco-elastic gelatin wedge. A comparison with natural observations shows interseismic and coseismic physics are captured in a robust, albeit simplified, way. This tool is used to validate that a continuum-mechanics based, visco-elasto-plastic numerical approach, typically used for large-scale geodynamic problems, can be extended to study the short-term seismogenesis of megathrust earthquakes. To generate frictional instabilities and match laboratory source parameters, a local invariant implementation of a strongly slip rate-dependent friction formulation is required. The resulting continuum approach captures several interesting dynamic features, including inter-, co- and postseismic deformation that agrees qualitatively with GPS measurements and dynamic rupture features, including cracks, self-healing pulses and fault re-rupturing. To facilitate a comparison to natural settings, I consider a more realistic setup of the Southern Chilean margin in terms of geometry and physical processes. Results agree with seismological, geodetic and geological observations, albeit for their coseismic speeds. They show a surprisingly good agreement with inter- and coseismic displacements measured before and during the 2010 M8.8 Maule earthquake. I further discuss on implications for several outstanding problems, including the contribution of cyclic to long-term deformation, physical mechanisms governing seismogenic zone limits and the low strength of megathrust faults. Finally, I demonstrate one of the main advantages of this approach; the spontaneous unstable rupturing of both on- and off-megathrust events. Simulated outerrise and splay and antithetic normal events geometrically resemble natural observations. They are triggered by megathrust-induced quasi-static stress changes and agree with analytical predictions of dynamic Coulomb wedge theory. Their impact is distinct, both on megathrust cycling, due to premature updip triggering of megathrust events, and for tsunami hazards that are increased due to steeply dipping off-megathrust fault planes. The innovative character of this seismo-thermo-mechanical approach opens a world of interdisciplinary research between geodynamics and seismology. This can relate to the generation and characteristics of megathrust earthquakes and beyond.